research article numerical analysis of dynamic...

Research ArticleNumerical Analysis of Dynamic Response of Corrugated CoreSandwich Panels Subjected to Near-Field Air Blast Loading

Pan Zhang Yuansheng Cheng and Jun Liu

School of Naval Architecture and Ocean Engineering Huazhong University of Science and Technology Wuhan 430074 China

Correspondence should be addressed to Jun Liu hustljhusteducn

Received 7 May 2014 Accepted 24 August 2014 Published 27 October 2014

Academic Editor Jeong-Hoi Koo

Copyright copy 2014 Pan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Three-dimensional fully coupled simulation is conducted to analyze the dynamic response of sandwich panels comprising equalthicknesses face sheets sandwiching a corrugated core when subjected to localized impulse created by the detonation of cylindricalexplosive A large number of computational cases have been calculated to comprehensively investigate the performance of sandwichpanels under near-field air blast loading Results show that the deformationfailure modes of panels depend strongly on stand-offdistance The beneficial FSI effect can be enhanced by decreasing the thickness of front face sheet The core configuration has anegligible influence on the peak reflected pressure but it has an effect on the deflection of a panel It is found that the benefits of asandwich panel over an equivalent weight solid plate to withstand near-field air blast loading are more evident at lower stand-offdistance

1 Introduction

Sandwich panels constructed from light face sheets and rela-tively low density cores are famous for the powerful ability tosupport bending load and to save structural weight Thepotential advantages of sandwich structures for shockmitiga-tion in both water and air blast have been exploited by someresearchers [1ndash3] but most works were focused on far-fieldblast and a less extent study is upon near-field air blast Inthe case of far-field blast shock fronts can be generally treatedwith acousticweak shock limit as the shockwaves attenuate toa soundwave and the impulse transmitted to an infinite rigidplate is twice that of incident shock wave due to the completeshock reflection A classic solution has been built by Taylor[4] to analyze the interaction between acoustic blast wave andfree-standing plate whereas the shock waves are character-ized with high intensity and spatially localization in the caseof near-field blast Moreover the nonlinear compressibilityeffects of air can further enhance the beneficial effects of FSIto reduce the impulse transmitted to structure [5ndash7]

Under high intensity blast loading the mechanical per-formance of metallic sandwich structures with several topol-ogy cores (such as square honeycomb [8 9] triangular hon-eycomb [10] hexagonal honeycomb [11 12] and pyramidal

lattice [13]) has been investigated Zhu et al [8] investigatedthe failure behaviors of honeycomb core sandwich panelunder either uniform or localized air blast loading Severaldistinct failure modes were identified Recent experimentalresults have revealed that the square honeycomb and pyra-midal lattice core sandwich panels suffer significantly smallerback face deflections than solid plates with identical masswhen subjected to high intensity air blast loading It is foundthat the benefits of square honeycomb core [9] and pyramidallattice core [13] sandwich panels over monolithic platesdiminish when the impulse intensity of shock wave isextremely highThis is due to the complete crush of core websat the center of panel and the dynamic fracture of front faces(as a result of the high strength of inertially stabilized trusses)Rimoli et al [14] applied a decoupled wet sand loadingmodeldeveloped by Deshpande et al [15] to simulate the dynamicresponse of edge-clamped corrugated core sandwich panelsand equivalent weight monolithic plates (made of 6061-T6aluminum alloy) subjected to wet sand blast loading A phe-nomenon of additional face sheet stretching and deflectionbetween corrugation web nodes was observed at high impul-sively blast loaded experiments Then Wadley et al [16]used a modified Johnson-Cook constitutive relation and

Hindawi Publishing CorporationShock and VibrationVolume 2014 Article ID 180674 16 pageshttpdxdoiorg1011552014180674

2 Shock and Vibration

140

150

372

175

Securely clampedDetonation point

Symmetry plane

All dimensions (mm)Symmetry plane

60∘

tf

tf

l

Hc

R

tc

Figure 1 Geometric models of the one-quarter corrugated sandwich panel and the one-quarter cylindrical explosive

Cockcroft-Latham failure criterion [17] to model the consti-tutive behavior of 6061-T6 aluminum alloy and adopted afully coupled simulation approach based on discrete particle-based method to make a detailed investigation into FSIeffects and fracturemechanisms of this complicatedmechan-ical problem The simulation results rationalized the localldquostreaksrdquo phenomenon which was arose from a local strongFSI effect and explained how dimples formed at the cornersof the test panels and well predicted panel failure at theclamped edges

Despite a great deal of work on blast performance of sand-wich panels mostly about far-field blast partly on the local-ized blast loading there are a few reports about the dynamicresponse of corrugated core sandwich panels under near-fieldair blast loadingThe aim of present study is to investigate thedynamic behavior of corrugated core sandwich panels sub-jected to highly intense near-field air blast loading and revealthe relationship between the structural performance metricsand geometry parameters by conducting numerical simula-tions

2 Geometry and Materials

The examined sandwich panels consist of two equal thicknessface sheets and corrugated core made of 304 stainless steelThe panels hold a given exposure area of 280mm times 300mmand the web of corrugated core keeps a constant inclinationangle of 60∘ Meanwhile the cylindrical TNT explosive is ofa radius of 175mm and a height of 372mm The geometricmodel of corrugated sandwich panels is depicted in Figure 1The geometric parameters of all sandwich panels consideredin this study are listed in Table 1 The calculated equivalentsolid plate thickness is listed in Table 2

For the face sheets and core webs of sandwich panelsmade of the same material the relative density 120588

119888

of core canbe expressed as

120588119888

=

119905119888

119905119888+ 119867119888cos120572

(1)

where 119905119888is the core web thickness 119867

119888is the core thickness

and 120572 is the inclination angle of core webThe material used to fabricate the corrugated sandwich

panels is annealed 304 stainless steel which has high workhardening potential under explosion loading Therefore theJohnson-Cook plasticity formulation which defines the flowstress as a function of equivalent plastic strain strain rateand temperature is employed in all simulationsThe dynamicflow stress is expressed by the following equation

120590119910= [119860 + 119861(120576

eq119901

)

119899

] [1 + 119888 ln(120576eq119901

1205760

)][1 minus (

119879 minus 119879119903

119879119898minus 119879119903

)

119898

]

(2)

where 120576eq119901and 120576

eq119901are equivalent plastic strain and equivalent

plastic strain rate respectively 119879 is the material temperature119879119903is the room temperature and 119879

119898is the melting temper-

ature of the material 119860 119861 119899 119888 1205760 and 119898 are Johnson-Cook

parameters determined by fitting to the experimental curvesThe material properties and the identified Johnson-Cookparameters [18] for the annealed 304 stainless steel are listedin Table 3 Although 304 stainless steel holds a desirable duc-tile performance to withstand the deformation produced byblast the sandwich panel will fail under severely loaded testscenariosTherefore the failure criterion of 304 stainless steelbased on the effective plastic strain is incorporated into num-erical model The rupture strain of material under impact isequal to 042 according to Ahn et alrsquos work [19]

Generally the surrounding air and the product of TNTexplosion are assumed to behave as ideal gasThe equation ofstate specified for ideal gas can be expressed as follows

119901 = (120574 minus 1) 1205881198921198900 where 120574 =

119862119901

119862V 1198900= 119862V119879 (3)

where 120574 is the adiabatic exponent 120588119892is the density of the gas

1198900is the internal energy 119862

119901and 119862V are the specific heat at

constant pressure and volume respectively and 119879 is the gas

Shock and Vibration 3

Table1Geometric

parametersa

ndsim

ulationresults

ofcompu

tatio

nalcases

considered

Case

number

SOD

Thickn

ess

Cellsize

Relativ

edensity

ofcore

Equivalent

solid

plate

thickn

ess

Peak

reflected

pressure

Maxim

ummom

entum

offro

ntface

Maxim

umdeflection

Failu

remod

e

119877 (mm)

Face

sheets

Core

Cell

wall

119897

(mm)

120588119888 ()

119905119904

(mm)

119901119903

(KPa)

119875

(kgtimes

ms)

Fron

tface

Back

face

Fron

tface

Back

face

119905119891

(mm)

119867119888

(mm)

119905119888

(mm)

120575119891

(mm)

120575119887

(mm)

mdashmdash

S20-1

3020

1732

1020

1035

579

53021times10

6546

mdash1619

Pitting

Pitting

S20-2

5020

1732

1020

1035

579

1300

0times10

6440

mdash1189

Pitting

Indenting

S20-3

8020

1732

1020

1035

579

29786times10

5284

760

377

Indenting

Mod

eIS20-4

100

20

1732

1020

1035

579

92518times10

4240

352

208

Indenting

Mod

eIS20-5

3020

1732

07

2074

8530

52770times10

6565

mdashmdash

Pitting

Pitting

S20-6

5020

1732

07

2074

8530

13002times10

6479

mdash1304

Pitting

Indenting

S20-7

8020

1732

07

2074

8530

29583times10

5312

1018

494

Indenting

Mod

eIS20-8

100

20

1732

07

2074

8530

92578times10

4274

411

267

Indenting

Mod

eIS20-9

3016

1732

1020

1035

500

47094times10

6495

mdashmdash

Pitting

Pitting

S20-10

5016

1732

1020

1035

500

12140times10

6460

mdash1354

Pitting

Indenting

S20-11

8016

1732

1020

1035

500

23078times10

5318

997

505

Indenting

Mod

eIS20-12

100

161732

1020

1035

500

85525times10

4246

509

281

Indenting

Mod

eIS20-13

3016

1732

07

2074

8450

46998times10

6518

mdashmdash

Pitting

Petalling

S20-14

5016

1732

07

2074

8450

12163times10

6495

mdash1576

Pitting

Indenting

S20-15

8016

1732

07

2074

8450

22944times10

5346

1285

678

Indenting

Mod

eIS20-16

100

161732

07

2074

8450

85567times10

4265

574

347

Indenting

Mod

eIS20-17

3012

1732

1020

1035

419

33315times10

6443

mdashmdash

Pitting

Petalling

S20-18

5012

1732

1020

1035

419

1000

4times10

6470

mdash1869

Pitting

Indenting

S20-19

8012

1732

1020

1035

419

21489times10

5345

1400

720

Indenting

Mod

eIS20-20

100

121732

1020

1035

419

83993times10

4283

771

427

Indenting

Mod

eIS20-21

3025

1732

1020

1035

679

55797times10

6554

mdashmdash

Pitting

Pitting

S20-22

5025

1732

1020

1035

679

13328times10

6423

2026

720

Indenting

Indenting

S20-23

8025

1732

1020

1035

679

30174times10

5290

547

278

Indenting

Mod

eIS20-24

100

25

1732

1020

1035

679

92833times10

4240

227

151

Mod

eIMod

eIS20-25

3020

1732

05

20546

495

52755times10

6597

mdashmdash

Pitting

Petalling

S20-26

5020

1732

05

20546

495

12955times10

6507

mdash1118

Pitting

Indenting

S20-27

8020

1732

05

20546

495

29245times10

5340

1174

583

Indenting

Mod

eIS20-28

100

20

1732

05

20546

495

89711times10

4305

615

383

Indenting

Mod

eIS28-1

3020

2425

1028

763

585

52730times10

6626

mdashmdash

Pitting

Pitting

S28-2

5020

2425

1028

763

585

12972times10

6542

mdash864

Pitting

Indenting

S28-3

8020

2425

1028

763

585

29478times10

5386

905

333

Indenting

Mod

eIS28-4

100

20

2425

1028

763

585

90553times10

4408

457

170

Indenting

Mod

eIS28-5

3020

2425

07

28546

532

52839times10

6585

mdashmdash

Pitting

Pitting

S28-6

5020

2425

07

28546

532

12950times10

6575

mdash1018

Pitting

Indenting

S28-7

8020

2425

07

28546

532

29364times10

5412

1115

456

Indenting

Mod

eIS28-8

100

20

2425

07

28546

532

90679times10

4327

516

240

Indenting

Mod

eI


Table1Con

tinued

Case

number

SOD

Thickn

ess

Cellsize

Relativ

edensity

ofcore

Equivalent

solid

plate

thickn

ess

Peak

reflected

pressure

Maxim

ummom

entum

offro

ntface

Maxim

umdeflection

Failu

remod

e

119877 (mm)

Face

sheets

Core

Cell

wall

119897

(mm)

120588119888 ()

119905119904

(mm)

119901119903

(KPa)

119875

(kgtimes

ms)

Fron

tface

Back

face

Fron

tface

Back

face

119905119891

(mm)

119867119888

(mm)

119905119888

(mm)

120575119891

(mm)

120575119887

(mm)

mdashmdash

S28-9

3016

2425

1028

763

505

47042times10

6587

mdashmdash

Pitting

Pitting

S28-10

5016

2425

1028

763

505

12155times10

6555

mdashmdash

Pitting

Pitting

S28-11

8016

2425

1028

763

505

23130times10

5409

1156

429

Indenting

Mod

eIS28-12

100

162425

1028

763

505

85910times10

4339

614

232

Indenting

Mod

eIS28-13

3016

2425

07

28546

452

47099times10

6619

mdashmdash

Pitting

Petalling

S28-14

5016

2425

07

28546

452

12130times10

6583

mdashmdash

Pitting

Pitting

S28-15

8016

2425

07

28546

452

23342times10

5435

1405

607

Indenting

Mod

eIS28-16

100

162425

07

28546

452

85914times10

4355

682

302

Indenting

Mod

eIS40-1

3020

3464

1040

546

589

52807times10

6714

mdashmdash

Pitting

Pitting

S40-2

5020

3464

1040

546

589

12993times10

6629

mdash77

9Pitting

Indenting

S40-3

8020

3464

1040

546

589

29633times10

5481

1120

270

Indenting

Mod

eIS40-4

100

20

3464

1040

546

589

91120times10

4408

620

144

Indenting

Mod

eIS40-5

3020

3464

07

40388

534

52818times10

674

1mdash

mdashPitting

Pitting

S40-6

5020

3464

07

40388

534

12993times10

6664

mdash614

Pitting

Indenting

S40-7

8020

3464

07

40388

534

29029times10

5504

1311

373

Indenting

Mod

eIS40-8

100

20

3464

07

40388

534

91133times10

4421

673

206

Indenting

Mod

eIS40-9

3016

3464

1040

546

509

46923times10

6686

mdashmdash

Pitting

Pitting

S40-10

5016

3464

1040

546

509

12123times10

6643

mdashmdash

Pitting

Pitting

S40-11

8016

3464

1040

546

509

23034times10

5493

1407

341

Indenting

Mod

eIS40-12

100

163464

1040

546

509

85560times10

4425

785

183

Indenting

Mod

eIS40-13

3016

3464

07

40388

454

47152times10

670

3mdash

mdashPitting

Pitting

S40-14

5016

3464

07

40388

454

12134times10

6665

mdashmdash

Pitting

Pitting

S40-15

8016

3464

07

40388

454

23274times10

5518

1659

482

Indenting

Mod

eIS40-16

100

163464

07

40388

454

85552times10

4438

846

263

Indenting

Mod

eI


Table 2 Simulation results of equivalent solid plates

Case number SOD Thickness Peak reflectedpressure Momentum Maximum

deflection Failure mode

119877

(mm)119905119904

(mm)119901119903

(KPa)119875

(kgtimesms)120575119904

(mm) mdash

SP-1 30 58 64101 times 106 1034 3034 Mode ISP-2 50 58 14147 times 106 891 1636 Mode IbSP-3 80 58 28021 times 105 726 775 Mode IbSP-4 100 58 92619 times 104 630 593 Mode IbSP-5 30 53 63730 times 106 1035 3357 Mode ISP-6 50 53 14122 times 106 893 1835 Mode IbSP-7 80 53 26578 times 105 730 860 Mode IbSP-8 100 53 92532 times 104 634 671 Mode IbSP-9 30 50 63287 times 106 1035 3573 Mode ISP-10 50 50 14073 times 106 894 1966 Mode IbSP-11 80 50 25159 times 105 732 928 Mode IbSP-12 100 50 92506 times 104 636 726 Mode IbSP-13 30 45 62330 times 106 1036 mdash PetallingSP-14 50 45 13990 times 106 897 2209 Mode IbSP-15 80 45 23856 times 105 737 1057 Mode IbSP-16 100 45 92358 times 104 641 824 Mode IbSP-17 30 42 61957 times 106 1037 mdash PetallingSP-18 50 42 13891 times 106 899 2374 Mode IbSP-19 80 42 22945 times 105 740 1141 Mode IbSP-20 100 42 92216 times 104 645 884 Mode IbSP-21 30 68 65412 times 106 1032 2524 Mode ISP-22 50 68 14334 times 106 886 1309 Mode IbSP-23 80 68 30678 times 105 719 614 Mode IbSP-24 100 68 93192 times 104 622 462 Mode Ib

Table 3 Material properties and Johnson-Cook parameters for the annealed 304 stainless steel [18]

120588

(kgm3)119864

(GPa) ] 119879119898

(K)119879119903

(K)119862

(JkgK)119860

(MPa)119861

(MPa) 119899 119888 1205760

119898

7900 200 03 1673 293 440 310 1000 065 007 100 100

temperature The material properties of air adopted are fromthe ANSYS-AUTODYNmaterial library shown in Table 4

Additionally the Jones-Wilkins-Lee (JWL) EOS which iscurrently in favor for hydrodynamic calculations of detona-tion product expansions is used to model the behavior ofTNT explosive This equation defines the pressure of det-onation product as a function of relative volume 120588

0120588 and

internal energy per initial volume 1198641198980 as shown in (4)

119901 = 1198601015840

(1 minus

120596120588119890

11987711205880

) 119890minus1198771(1205880120588119890)

+ 1198611015840

(1 minus

120596120588119890

11987721205880

) 119890minus1198772(1205880120588119890)

+

120596120588119890

1205880

1198641198980

(4)

where 119901 is the blast pressure 120588119890and 120588

0are the density of

the explosive and explosive products respectively and 1198641198980

isspecific internal energy of the explosive The parameters

Table 4 Material properties of air [20]

120588

(kgm3)119879

(K)119862

(JkgK) 1205741198900

(kJkg)1225 2882 7176 14 2068 times 105

1198601015840

1198611015840

1198771 1198772 and 120596 are material constants which are related

to the type of explosive The material properties adopted forthe TNT explosive are also from the ANSYS-AUTODYNmaterial library shown in Table 5

3 Numerical Model and Validation

31 Numerical Model The sandwich panels are peripherallyclamped Due to the symmetry of structure and loading con-dition only one-quarter of the corrugated sandwich panel


Table 5 Material properties of TNT explosive [20]

120588

(kgm3)1198601015840

(GPa)1198611015840

(GPa) 1198771

1198772

120596

C-Jdetonationvelocity(ms)

C-Jenergyunitvolume(kJm3)

C-J pressure(kPa)

1630 37377 375 415 09 035 6930 60 times 106 21 times 107

Flow out boundaryAir

TNT explosivePanel

Figure 2 View of three-dimensional finite element model andhigh-resolution view of the field around sandwich panel (Forinterpretation of the references to colour in this figure legend thereader is referred to the web version of this paper)

and cylindrical explosive are modeled in simulations Thethree-dimensional numerical model used in this study isshown in Figure 2

Both the face sheets and core are meshed using 1mmBelytschko-Tsay shell element based on Mindlin plate theory[20] Meanwhile the surrounding air is modeled using Euler-Godunov solver which is a second-order multimaterial Eulersolver with the default SLIC (simplified line interface cal-culation) transport scheme in ANSYS-AUTODYN and thecylindrical charge fills in the part of the surrounding air Boththe contact between the core cell wall and the face sheets dueto the plastic buckling and the self-contact of the core walldue to cell wall folding are taken into account in simulationsIn addition the Eulerian meshes fully couple with the shellelements During the process of coupling the Euler cellsintersected by the Lagrange interface define a stress profilefor the Lagrange boundary vertices In return the Lagrangeinterface defines a geometric constraint to the flowofmaterialin the Euler gridThe parameter named ldquocover fraction limitrdquois used to determine when a partially covered Euler cell isblended to a neighbor cellThe value of cover fraction limit isset to 05 During the discrete process the size of the smallestcell in the surrounding Euler grid should be at most one halfof the artificial thickness of shell element to guarantee theFSI effect In addition the mesh of surrounding air is biasedtowards the field near to sandwich panels (shown in Figure 2)The mesh optimization has been executed to make a trade-off between the results of computation and the computationefficiency

Numerical oscillation

Exponential decay

Time of arrival

times104

4

3

2

1

0

Pmax

000 005 010 015 020

Time (ms)

Pres

sure

(kPa

)

Figure 3 History of the air-blast induced pressure at the stand-offdistance of 30mm

32 Validation

321 Free Field Air Blast Pressure The 2D axial symmetrymodel with a very fine Eulerian mesh is used to simulate thedetonation and expanding process of a 55 g spherical explo-sive placed in an infinity atmosphere field Figure 3 showsthe pressure-time history of a gauge point positioned at astand-offdistance of 30mm It is found that a slight numericaloscillation of pressure appeared after the pressure reaches thepeak value and followed by exponential decay The impulsecarried by shock wave as a key factor to determinate thedeflection of blast loaded plates can be calculated by thetime integration of pressure It is believed that the error dueto numerical oscillation exerts a weak influence on the areaunder the pressure line

A comparison is made between the simulation resultsand the predicting values of the fitting equation developedby Kinney and Graham [21] in terms of the peak pressureof stand-off distances with range from 30mm to 200mm asshown in Figure 4 It is clear that the numerical results arevery close to the predicting values

322 StructureBlast Interaction A series of experiments ofclamped mild steel quadrangular plates to localized air blastloading were conducted by Jacob et al [22] The test plateswere made of mild steel and cut from the shelf cold rolledplates The blast loading was generated by the detonation of aplastic explosive with circular dish shape The plastic explo-sive was placed at the center of a polystyrene foam pad withthickness of 12mm and detonated by a short stub detonatorwithmass of 1 gThemass of charge is in the range of 35ndash45 g

Shock and Vibration 7Pe

ak p

ress

ure (

kPa)

Simulation resultsKinney and Graham

Stand-off distance (mm)40 80 120 160 200

times104

4

3

2

1

0

Figure 4 Peak pressure versus stand-off distance for simulationresults and the fitting equation developed by Kinney and Graham[21]

Therefore the damage power of detonator should be takeninto account in simulations But the outline of the detonatorwas not given The charge height was changed to ensurethat the weight of the charge modeled in simulation wasequal to the summation of the weight of detonator and thecharge used in experiments However this would result in anoverprediction of the damage power of detonator as a resultof that the stand-off distance between the plate and detonatoris smaller

To intuitively validate the numerical approach usedin this study five experimental cases possessing detailedpostmortem profiles are selected to simulate the dynamicresponse process using ANSYS-AUTODYN Exposed area ofthose impacted square plates is 190mm times 129mm and thethickness of the plates is 16mm The material coefficientsused to model the dynamic mechanical behavior of impactedplates are given by Jacob et al [22] The one-quarter finiteelement models of a test plate and air field are shown inFigure 5 The finite element model of plate consists of 5000quadrilateral elements while the finite element model of airfield consists of 1000000 hexahedral elements

Figure 6 shows the cross-sectional profiles of experimentsand numerical simulations in each case It is observed thatpartial tearing appeared in the central area both in theexperiment and simulation for the test case of N01100122and the predicted profiles are closely similar to experimentalresults The comparison of predicted center point deflectionsand measured values is presented in Table 6 The simulationresults fit well with the experimental results except smalloverestimation observed in simulations The main reason isthat the damage power of detonator is overpredicted It isconcluded that the numerical method adopted in the simu-lations is accurate enough which is expected to be applied inthe dynamic analysis of complex constructions to near-fieldair blast loading such as sandwich panels

Figure 5 One-quarter finite element models of quadrangular plateand air field

(a)

(b)

Figure 6 Comparison of cross sectional profiles of (a) experiments[22] and (b) proposed simulations The test numbers from bottomto top are N021100124 N01100123 N22100145 N01100121 andN01100122

4 Numerical Simulation Results

Using sandwich panel for impact mitigation the protectingconstruction designers generally assess the performance ofsandwich panel from following aspects impulse on front


Table 6 Experimental and numerical results for selected cases

Test number Mass of charge(g)

Experimental displacement(mm)

Numerical displacement(mm)

Relative error()

N02100124 35 204 228 118N01100123 38 214 252 178N01100121 40 237 267 127N22100145 39 234 259 107N01100122 45 Tearing Tearing mdash

(a) 119905 = 0 120583s (b) 119905 = 43 120583s (c) 119905 = 70 120583s

(d) 119905 = 121 120583s (e) 119905 = 270 120583s (f) 119905 = 454 120583s

Figure 7 AUTODYN screenshots showing the transient response of the detonation products and the sandwich panel (case number S20-1)

plate permanent deflections history of pressure near or onthe FSI surface and the deformationfailure patterns

Figure 7 shows typical results of the fully coupled cal-culation revealing the interaction between the explosivegas products and the sandwich panel (Case number S20-1) Figure 7(a) gives the initial state of the explosive andsandwich panel at t = 0 The cylindrical explosive is instantlyignited at this moment by the detonator placed at the centerpoint of the top face of charge At 119905 = 43 120583s the explosivegas products abruptly expand outward to compress thesurrounding air and then begin to interact with the front

surface of sandwich panel at 119905 = 70 120583s Once interactingthe sandwich panel acts as flow boundary for the expandedexplosive products reversely which exert pressure load onstructure At the initial stage of fluid-structure interactionthe sandwich panel nearly keeps undeformed for two reasons(1) the impartedmomentum to sandwich panel is not enoughlarge and (2) the structural response behaves a degree of timehysteresis A dent failure is firstly formed at the central areaof sandwich front face at 119905 = 121 120583s which has been alsofound by Zhu et al [23] After that the deformation extendsoutwards and downwards with the transferring of impulse


DelaminationCreaseCrease

Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(a) Front face

Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(b) Back face

Tearing failure

Plastic bucklingElastic buckling

Stretching

First cellSecond cell Third cell

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(c) Corrugated core

Figure 8 Deformation and failure patterns of a sandwich panel (case number S20-1) (For interpretation of the references to colour in thisfigure legend the reader is referred to the web version of this paper)

The front face deforms continually to slap into the back face at119905 = 270 120583s In this process the middle core webs provide theresistance force to the front face and begin to crush Due tothe large stretching and bending deformation the front facefails at the joint between the front face sheet and middle coreweb and then the explosive products permeate into the innerspace of cell As the simulation proceeding the face sheetsand the core continue to deform under their inertia shownin Figure 7(f) and the contact detected between them doesits work in subsequent process till the contact force reducesto 0

After the slight oscillation of the sandwich panel dueto the occurrence of spring back effect all kinetic energyof the structure is dissipated by the plastic bending andstretching of face sheets and the crushing of corrugated coreThe final material status and deformationfailure patternsof a panel are shown in Figure 8 Overall most part of thesandwich panel sinks into plastic status In the central portionof front and back face sheets the pitting failure which ischaracterized by a localized pit and fracture on the surface

occurs and significant tearing failure is observed on both thefront and back faces along the middle ridge of corrugatedcore shown in Figures 8(a) and 8(b) Careful examinationshows that some creases are formed on front face along thoseridges of corrugated core owing to the localized supportingforce of core web and delamination failure between the frontface and core also occurs as indicated in Figure 8(a) Underthe loading force of pressured explosive products the frontface gains considerable momentum away from blast locationand undergoes extremely large stretching deformation whichleads central part material to failing and the eroding effectbased on geometric strain is applied to those excessivelydistorted elements Figure 8(c) illustrates the failure modeof a corrugate core under near-field air blast loading Thecrushing strains of corrugated core webs in the centralportion are greatest enough to fail because of the greatestapplied pressure associated with the charge location Thewebs of the second (sorted from center to outskirts) cellundergo remarkable plastic buckling deformation mean-while the webs of the third cell undergo elastic buckling


Solid platePanel front facePanel back face

Material failed

Defl

ectio

n (m

m)

Distance from center of plate (mm)

35

30

25

15

20

10

5

00 20 40 60 80 100 120 140

(a)


Defl

ectio

n (m

m)


35

30

25

15

20

10

5

0

0 20 40 60 80 100 120 140

Material failed

(b)

Figure 9 Sandwich panel (case number S20-1) and solid plate (case number SP-1) sectioned profiles predicted along (a) the directionperpendicular to corrugations and (b) the direction parallel to corrugations

deformation whereas the others nearly remain undeformedThe failure modes of the panels and solid plates tested hereinare identified and listed in Tables 1 and 2 respectively

The predicted sectioned half profiles along the directionsparallel to corrugations and perpendicular to corrugationsare plotted in Figure 9 for the sandwich panel and equivalentweight monolithic plate under the same air blast loadingThe midpoint of back face of sandwich panel only undergoeshalf deflection of solid plate midpoint The difference valuebetween the front face and back face deflections reveals thatthe core crushing effect is outstanding in the center area butvanishes in the outskirts field under near-field air blast Asignificant local bending deformation superimposes on theglobal bending deformation of front face along the directionperpendicular to corrugations in the center field The globalinelastic deformation plays a dominative role in the exteriorzone of front face The local bending deformation is not clearon the back face and front face (along the direction parallel tocorrugations) It is also found that the material of center fieldof front face sheet fails under this high-intensity loading andthe tearing failure occurs on the back face between the firstcell core webs (Figure 8(b))

In order to better understand FSI effect the distributionsof pressure are investigated both temporally and spatiallySeveral pressure gauges are intentionally placed in air fieldabove the shock impacted plates along the axis of cylindricalcharge The exact locations of those pressure gauges areshown in Figure 10The location of Gauge 1 is firstly occupiedby the undeformed test plate at initial state and Gauge 2is placed near the FSI surface to measure the pressure ofthe reflected shock wave The distances between the adjacentgauges are equal to 2mm The pressure-time histories of fivepressure gauges for a sandwich panel (case number S20-1)and an equivalent weightmonolithic plate (case number SP-1)

Shock impacted plate Neutral plane

Detonation point

Cylindrical charge

Axis of cylindricalcharge

Gauge 2Gauge 1

Gauge 3Gauge 4Gauge 5

Figure 10 Locations of pressure gauges placed

under the same explosion loading are shown in Figure 11Theincidentwave travels forward viaGauge 5 firstly It is observedfromGauges 2ndash5 that the pressure jump phenomenon for theincident wave is not evident But this phenomenon ordinarilyexists in far-field explosion This is due to the fact that theimpacted plate restricts the expansion of explosive productsThose air particles close to FSI surface like those aroundGauges 2ndash5 have been rapidly compressed due to the expan-sion of explosive production leading to increase of pressureTherefore at the initial phase the increase of pressure ofthe locations Gauges 2ndash5 is induced not only by the high-pressure incident shock front but also by the highly nonlinearcompression of air medium The pressure of reflected wavedeserves more attention because it is the effective loadingon structure Using a solid plate (case number SP-1) as abenchmark the sandwich panel (case number S20-1) givesa decrease of peak reflected pressure by 173 as a result ofthe beneficial FSI effect It is noticeable that the pressure-time



Gauge 4Gauge 5

times106

6

5

4

3

2

1

0

000 001 002 003

Time (ms)

Pres

sure

(kPa

)

(a)

times106

6

5

4

3

2

1

0

Pres

sure

(kPa

)

000 001 002 003

Time (ms)


Gauge 4Gauge 5

(b)

Figure 11 Pressure-time history of gauges placed in air field along the axis of cylindrical charge for the test plates (a) Sandwich panel (casenumber S20-1) and (b) solid plate (case number SP-1)

curves of Gauges 3ndash5 hold a double-humped feature Gauge 3is characterized by a high hump for reflected shock and a lowhump for incident shock As the decay of the reflected shockwave the characteristics of Gauges 4-5 are just reverse to thatof Gauge 3 And the pressure of Gauge 1 increases abruptly asthe explosive products flow into the field occupied by the testplates initially

Figure 12 shows that the peak reflected pressure decaysvery fast from center to outside It conforms that sandwichpanel construction with light face sheet can reduce the reflec-ted pressure However this benefit of the sandwich panelconstruction over an equivalent weight solid plate is evidentonly in the center field of plate under near-field air blastloading It is shown that the locality characteristic inferredfrom the deformation pattern is not exhibited in pressurefield

5 Discussions

The performance of corrugated core sandwich panels underexplosion loading is closely related to the geometric param-eters of panels In this research a parametric study isconducted to reveal the relationship between the key charac-teristics (deformationfailure impulse transmitted and peakpressure near FSI surface) of structural response and severalspecific geometry parameters (stand-off distance face sheetthickness cell size and core web thickness relative densityof core) The results of parametric study are presented in thissection

51 Effect of Stand-off Distance To investigate the effect ofstand-off distance on the deformationfailure pattern and thereflected pressure all panel configurations and solid plates

considered here are subjected to the air blast loading createdby the detonation of the TNT charge with a given mass but atstand-off distances of 30mm 50mm 80mm and 100mmrespectively

Figure 13 shows the final deformationfailure patterns ofthe sandwich panels with the same face sheet thickness (119905

119891=

20mm) and core web thickness (119905119888= 10mm) but different

cell sizes (119897 = 20 28 and 40mm resp) and equivalent weightsolid plates under different stand-off distances It is foundthat the failure modes of front face turn from the pitting fail-ure to indenting failure with the increase of stand-off distanceand that those of back face turn from the pitting failure andpetalling failure to the global dome failure (Mode I failure)Meanwhile the failure modes of equivalent solid plates turnfrom the global dome failure attached by an inner dome tojust the global dome failure Additionally the failure area ofstructures is larger at lower stand-off distance As expectedthe center deflections of sandwich front face back face andsolid plates decreasewith the increase of stand-off distance asshown in Figure 14The plot illustrates that the benefits of thesandwich panel construction over a solid plate to withstandblast loads are clearly evident with smaller back plate deflec-tions compared with the equivalent weight solid plates sub-jected to the same loads However the explosion loading fora given charge mass at lower stand-off distance exhibits highintensity and spatial localization And the back faces of somesandwich panel configurations are likely to fail under thisloadingTherefore the benefits of sandwich panel will vanishin this case Figure 13 shows that tearing damage occurs onthe back face of sandwich panels with cell sizes of 28mmand 40mm subjected to the explosion loading at the stand-off distance of 30mm Careful examination shows that somestreaks are formed on front face between the core webs owingto the effect of a locally strong FSI shown in Figure 13


Distance from center of plate (mm)0 20 40 60 80 100 120 140

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

Solid plateSandwich panel

(a)

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)



(b)

Figure 12 Spatial distributions of peak reflected pressure near the FSI surface along (a) the direction perpendicular to corrugations and (b)the direction parallel to corrugations

SOD = 30 mm SOD = 50 mm SOD = 80 mm SOD = 100mm

Increasing stand-off distance

(a)


(b)


(c)


(d)

Figure 13 Cross-sectional view of the deformationfailure modes of sandwich panels and equivalent solid plates under different stand-offdistances (a) 119905

119891

= 20mm 119905c = 10mm and 119897 = 20mm (b) 119905119891

= 20mm 119905119888

= 10mm and 119897 = 28mm (c) 119905119891

= 20mm 119905119888

= 10mm and119897 = 40mm (d) 119905

119904

= 58mm

The peak reflected pressure of the FSI surface is animportant index for quantitatively analyzing the benefits ofthe FSI effect Figure 15 shows the peak reflected pressure ofthe air particle placed at the center point of the sandwichpanel front faces and the solid plates Those sandwich panelswith the same core configuration (119905

119888= 10mm 119897 = 20mm)

but different face sheet thicknesses (119905119891= 12mm 16mm

20mm and 25mm) are chosen to contrast with equivalentsolid plates It is found that the sandwich panel with a lower

peak reflected pressure performs better than the equivalentweight solid plate as a result of the lower inertia of sandwichpanel front face This benefit of sandwich construction ismore remarkable for air blast loading at lower stand-offdistance and the influence rule of stand-off distance onpeak reflected pressure is the same for panels with differentface sheet thicknesses Using the equivalent solid plates asa benchmark these four sandwich panels with face sheetthicknesses of 12mm 16mm 20mm and 25mm lead to

Shock and Vibration 13M

axim

um d

eflec

tion

(mm

)

Stand-off distance (mm)

Solid plate

Cell size = 20 mmCell size = 28 mm

Cell size = 40 mm Equivalent solid plate

Front face

Back face

35

100755025

30

25

20

10

5

0

15

Figure 14 Comparison of the center deflection of the sandwichpanel front face back face and equivalent weight solid plate versusthe stand-off distance 119905

119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm

a decrease in the peak reflected pressures by 4623 25591729 and 147 at the stand-off distance of 30mm 27981374 811 and 702 at the stand-off distance of 50mm635 827 071 and 164 at the stand-off distance of80mm and 892 755 011 and 039 at the stand-offdistance of 100mm respectively

52 Effect of Face Sheet Thickness The thickness of front facesheet is critical to the FSI effect Therefore the investigationof the effect of face sheet thickness is necessary to reveal someinherent laws to guide the design of corrugated core sandwichpanel

As indicated in Figure 15 the thickness of front facehas a significant influence on the peak reflected pressure Ifthe thickest front face (25mm) is adopted as a benchmarkthe other front faces (12mm 16mm and 20mm) give adecrease of peak reflected pressure by 4029 156 and498 at stand-off distance of 30mm 2494 891 and246 at stand-off distance of 50mm 2878 2352 and129 at stand-off distance of 80mm and 952 787and 034 at stand-off distance of 100mm respectively Thebenefit of FSI effect for sandwich construction is enhancedgreatly as the reduction of face sheet thicknessMoreover thiseffect of face sheet thickness is more outstanding under near-field explosion condition

To investigate the effect of face sheet thickness on thecenter deflection of front face and back face the results ofthe sandwich panels with the same core configuration (119905

119888=

10mm 119897 = 20mm) and varied face sheet thicknesses (119905119891=

12mm 16mm 20mm and 25mm) are shown in Figure 16With the increase of the face sheet thickness the deflectionsof midpoint reduce especially under the near-field explosionloading but it is an important issue for a designer to deal withthe confliction properly between the stiffness and weight

tf = 12 mmtf = 16 mmtf = 20 mmtf = 25 mm

ts = 42mmts = 50mmts = 58mmts = 68mm

times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100


Figure 15 Comparison of the peak reflected pressure (near the FSIsurface) of sandwich panels and equivalent weight solid plates versusthe stand-off distance For sandwich panels 119905

119888

= 10mm and 119897 =20mm

53 Effect of Core Configuration The core configuration con-tains the core web thickness cell size and relative density ofcore All of them play a notable role in the impact mitigationeffect of corrugated core sandwich panel

The peak reflected pressure of sandwich panels with thesame face sheet thickness (119905

119891= 20mm) but different core

web thicknesses (119905119888= 10mm 07mm and 05mm) and dif-

ferent cell sizes (119897 = 20mm 28mm and 40mm) is plotted inFigure 17 At first glance there is a complete overlap amongthose peak reflected pressure stand-off distance curves It isconcluded that the variations of the core web thickness andcell size result in a negligible change of peak reflected pressureof the midpoint of front face However the core works as afoundation for the front face and simultaneously works as aloading transporter for the back face The configuration of

14 Shock and VibrationM

axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100


Front facetf = 12 mmtf = 16 mmtf = 20 mmtf = 25 mm

Back facetf = 12 mmtf = 16 mmtf = 20 mmtf = 25 mm

Figure 16Maximumdeflections of sandwich panels with same coreconfiguration (119905

119888

= 10mm 119897 = 20mm)

core can considerably affect the deformation of front faceand back face It can be observed from Figure 14 that forgiven face sheet thickness and core web thickness largercell sizes (larger core thicknesses for the given inclinationangle of 60∘) result in smaller back face deflections and largerfront face deflections The failure mode of back face is a typeof global deformation the deformation of back face mostlydepends on the global bending resistance of sandwich panelThe larger cell sizes have high rigidity in flexure resulting ina smaller back face deflection under blast loading Howeverthe failure pattern of front face deflection is a type of centrallocalized failure and is dominated by localized deflectionThemaximum deflections of front face are related to the localstiffness of the central field As the increase of cell sizesthe central field between two core webs becomes weak instiffness This is the reason that larger cell sizes result inlarger front face deflections For a given cell size the effectof core web thickness on deformation is shown in Figure 18As expected the deflections of front face and back face reducewith the increase of core web thickness which results in theenhancement of global bending resistance and local stiffnessof sandwich panel

As illustrated previously the crushing mechanism of coremedia is mostly dependent on the relative density of coreThe relative density of core is determined by the core webthickness and the cell size However the relative densityof core has no significant influence on the peak reflectedpressure as inferred from Figure 17

Figure 19 shows the maximum deflections of sandwichpanels (S20-25simS20-28 S28-5simS28-8 and S40-1simS40-4) withdifferent cell sizes and core web thicknesses but the samerelative density of core (546) The variation tendency offront face deflections is not as clear as that of back face For a

times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)

tc = 10 mmtc = 07 mmtc = 05 mm

(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100


Cell size = 20mmCell size = 28mmCell size = 40mm

(b)

Figure 17 Peak reflected pressure of midpoint of sandwich panelswith (a) different core web thicknesses and with (b) different cellsizes

given relative density the cell size plays a leading role in theinfluence of back face deflections

Figure 20 shows the maximum deflections of back face ofthree sandwich panels with similar weight (ie the equivalentsolid plates thicknesses are 579mm 585mm and 589mmresp) but different relative density of core (ie 1035 763and 546 resp) subjected to the same blast loading It isfound that the back face deflections increase with the increaseof core relative density especially at lower stand-off distance


25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)


Front facetc = 10 mmtc = 07 mmtc = 05 mm

Back face

Figure 18 Maximum deflections of front face and back face ofsandwich panels with different core web thicknesses

30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)

Front faceS20-25simS20-28S28-5simS28-8S40-1simS40-4

Back faceS20-25simS20-28S28-5simS28-8S40-1simS40-4

Figure 19 Maximum deflections of sandwich panels with the samerelative density (546)

6 Conclusions

A detailed numerical analysis based on fully coupled numer-ical method is presented aiming to reveal the interactionbetween the explosive gas product and sandwich panel Theimportant role of the nonlinear compression of air mediumplayed in beneficial FSI effect under near-field air blast isrevealed by investigating the distributions of shock wavepressure both temporally and spatially It is concluded thatthe nonlinear compression effect is significant under near-field air blast Under near-field air blast loading the frontface of sandwich panel undergoes a significant local bending

120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)

Figure 20 Maximum deflections of back face of sandwich panelswith different relative density of core

deformation which leads to the occurrence of streak typedeformation between core webs in the center field while thedeformation pattern of back face is determined by globalbending deformation

The parametric study shows that the failure modes ofsandwich panels depend strongly on stand-off distance Andthe failure area increases with the decrease of stand-off dis-tance The benefits of sandwich construction over solid plateto withstand blast loads are clearly evident with lower backplate deflections and lower peak reflected pressures comparedwith the equivalent weight solid plates subjected to the sameload It is found that those benefits are more evident at lowerstand-off distance As the reduction of face sheet thicknessthe benefit of FSI effect of sandwich construction is enhancedgreatly and the deflections of sandwich front face and backface increase The sandwich panels with a light face sheetare more likely to fail Therefore it is essential to optimizethe configuration of sandwich panel to keep back face fromdamage failure The core configuration has a negligible influ-ence on the peak reflected pressure By adopting larger cellsizes and thicker core webs the deflections of back faces canbe reduced For a given areal density of sandwich panel theback face deflections increase with the increase of corerelative density

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The reported research is supported by the National Nat-ural Science Founding of China (under the Contract no51209099) and the Supporting Technology Funding of Ship-building Industry The financial contributions are herebygratefully acknowledged


References

[1] Z Xue and J W Hutchinson ldquoPreliminary assessment of sand-wich plates subject to blast loadsrdquo International Journal ofMech-anical Sciences vol 45 no 4 pp 687ndash705 2003

[2] L Yueming A V Spuskanyuk S E Flores et al ldquoThe responseof metallic sandwich panels to water blastrdquo Journal of AppliedMechanics Transactions ASME vol 74 no 1 pp 81ndash99 2007

[3] Z Xue and J W Hutchinson ldquoA comparative study of impulse-resistant metal sandwich platesrdquo International Journal of ImpactEngineering vol 30 no 10 pp 1283ndash1305 2004

[4] G I Taylor ldquoThe pressure and impulse of submarine explosionwaves on platesrdquo in The Scientific Papers of Sir Geoffrey IngramTaylor Aerodynamics and the Mechanics of Projectiles andExplosions G K Batchelor Ed vol 3 pp 287ndash301 CambridgeUniversity Press Cambridge UK 1963

[5] N Kambouchev L Noels and R Radovitzky ldquoNonlinear com-pressibility effects in fluid-structure interaction and their impli-cations on the air-blast loading of structuresrdquo Journal of AppliedPhysics vol 100 no 6 Article ID 063519 2006

[6] N Kambouchev L Noels and R Radovitzky ldquoNumerical simu-lation of the fluid-structure interaction between air blast wavesand free-standing platesrdquo Computers and Structures vol 85no 11-14 pp 923ndash931 2007

[7] N KambouchevAnalysis of blast mitigation strategies exploitingfluid-structure interaction [PhD thesis]Massachusetts Instituteof Technology Cambridge Mass USA 2007

[8] F Zhu G Lu D Ruan and D Shu ldquoTearing of metallic sand-wich panels subjected to air shock loadingrdquo Structural Engineer-ing and Mechanics vol 32 no 2 pp 351ndash370 2009

[9] K P Dharmasena H N G Wadley Z Xue and J W Hutchin-son ldquoMechanical response of metallic honeycomb sandwichpanel structures to high-intensity dynamic loadingrdquo Interna-tional Journal of Impact Engineering vol 35 no 9 pp 1063ndash1074 2008

[10] Z Wei V S Deshpande A G Evans et al ldquoThe resistance ofmetallic plates to localized impulserdquo Journal of the Mechanicsand Physics of Solids vol 56 no 5 pp 2074ndash2091 2008

[11] G N Nurick G S Langdon Y Chi andN Jacob ldquoBehaviour ofsandwich panels subjected to intense air blast Part 1 Experi-mentsrdquo Composite Structures vol 91 no 4 pp 433ndash441 2009

[12] D Karagiozova G N Nurick andG S Langdon ldquoBehaviour ofsandwich panels subject to intense air blastsmdashpart 2 numericalsimulationrdquo Composite Structures vol 91 no 4 pp 442ndash4502009

[13] K P Dharmasena H N G Wadley K Williams Z Xue andJ W Hutchinson ldquoResponse of metallic pyramidal lattice coresandwich panels to high intensity impulsive loading in airrdquoInternational Journal of Impact Engineering vol 38 no 5 pp275ndash289 2011

[14] J J Rimoli B Talamini J J Wetzel K P Dharmasena RRadovitzky andH N GWadley ldquoWet-sand impulse loading ofmetallic plates and corrugated core sandwich panelsrdquo Interna-tional Journal of Impact Engineering vol 38 no 10 pp 837ndash8482011

[15] V S Deshpande R MMcMeeking H N GWadley and A GEvans ldquoConstitutive model for predicting dynamic interac-tions between soil ejecta and structural panelsrdquo Journal of theMechanics and Physics of Solids vol 57 no 8 pp 1139ndash11642009

[16] HNGWadley T Borvik L Olovsson et al ldquoDeformation andfracture of impulsively loaded sandwich panelsrdquo Journal of theMechanics and Physics of Solids vol 61 no 2 pp 674ndash699 2013

[17] M Cockcroft and D Latham ldquoDuctility and the workability ofmetalsrdquo Journal of the Institute ofMetals vol 96 no 1 pp 33ndash391968

[18] S Lee F Barthelat J W Hutchinson and H D EspinosaldquoDynamic failure of metallic pyramidal truss core materialsmdashexperiments and modelingrdquo International Journal of Plasticityvol 22 no 11 pp 2118ndash2145 2006

[19] D-G Ahn G-J Moon C-G Jung G-Y Han and D-Y YangldquoIMPACT behavior of A STS 304H sheet with a thickness of 07MMrdquo Arabian Journal for Science and Engineering vol 34 no1 pp 57ndash71 2009

[20] AUTODYN Theory Manual Revision 43 Century DynamicsConcord Mass USA 2005

[21] G F Kinney andK J Graham Explosive Shocks in Air SpringerNew York NY USA 2nd edition 1985

[22] N Jacob K Y Chung G N Nurick D Bonorchis S A Desaiand D Tait ldquoScaling aspects of quadrangular plates subjectedto localised blast loadsmdashexperiments and predictionsrdquo Interna-tional Journal of Impact Engineering vol 30 no 8-9 pp 1179ndash1208 2004

[23] F Zhu L Zhao G Lu and E Gad ldquoA numerical simulation ofthe blast impact of square metallic sandwich panelsrdquo Interna-tional Journal of Impact Engineering vol 36 no 5 pp 687ndash6992009

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VLSI Design



Shock and Vibration


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Propagation




Navigation and Observation



DistributedSensor Networks



140

150

372

175

Securely clampedDetonation point

Symmetry plane

All dimensions (mm)Symmetry plane

60∘

tf

tf

l

Hc

R

tc

Figure 1 Geometric models of the one-quarter corrugated sandwich panel and the one-quarter cylindrical explosive

Cockcroft-Latham failure criterion [17] to model the consti-tutive behavior of 6061-T6 aluminum alloy and adopted afully coupled simulation approach based on discrete particle-based method to make a detailed investigation into FSIeffects and fracturemechanisms of this complicatedmechan-ical problem The simulation results rationalized the localldquostreaksrdquo phenomenon which was arose from a local strongFSI effect and explained how dimples formed at the cornersof the test panels and well predicted panel failure at theclamped edges

Despite a great deal of work on blast performance of sand-wich panels mostly about far-field blast partly on the local-ized blast loading there are a few reports about the dynamicresponse of corrugated core sandwich panels under near-fieldair blast loadingThe aim of present study is to investigate thedynamic behavior of corrugated core sandwich panels sub-jected to highly intense near-field air blast loading and revealthe relationship between the structural performance metricsand geometry parameters by conducting numerical simula-tions

2 Geometry and Materials

The examined sandwich panels consist of two equal thicknessface sheets and corrugated core made of 304 stainless steelThe panels hold a given exposure area of 280mm times 300mmand the web of corrugated core keeps a constant inclinationangle of 60∘ Meanwhile the cylindrical TNT explosive is ofa radius of 175mm and a height of 372mm The geometricmodel of corrugated sandwich panels is depicted in Figure 1The geometric parameters of all sandwich panels consideredin this study are listed in Table 1 The calculated equivalentsolid plate thickness is listed in Table 2

For the face sheets and core webs of sandwich panelsmade of the same material the relative density 120588

119888

of core canbe expressed as

120588119888

=

119905119888

119905119888+ 119867119888cos120572

(1)

where 119905119888is the core web thickness 119867

119888is the core thickness

and 120572 is the inclination angle of core webThe material used to fabricate the corrugated sandwich

panels is annealed 304 stainless steel which has high workhardening potential under explosion loading Therefore theJohnson-Cook plasticity formulation which defines the flowstress as a function of equivalent plastic strain strain rateand temperature is employed in all simulationsThe dynamicflow stress is expressed by the following equation

120590119910= [119860 + 119861(120576

eq119901

)

119899

] [1 + 119888 ln(120576eq119901

1205760

)][1 minus (

119879 minus 119879119903

119879119898minus 119879119903

)

119898

]

(2)

where 120576eq119901and 120576

eq119901are equivalent plastic strain and equivalent

plastic strain rate respectively 119879 is the material temperature119879119903is the room temperature and 119879

119898is the melting temper-

ature of the material 119860 119861 119899 119888 1205760 and 119898 are Johnson-Cook

parameters determined by fitting to the experimental curvesThe material properties and the identified Johnson-Cookparameters [18] for the annealed 304 stainless steel are listedin Table 3 Although 304 stainless steel holds a desirable duc-tile performance to withstand the deformation produced byblast the sandwich panel will fail under severely loaded testscenariosTherefore the failure criterion of 304 stainless steelbased on the effective plastic strain is incorporated into num-erical model The rupture strain of material under impact isequal to 042 according to Ahn et alrsquos work [19]

Generally the surrounding air and the product of TNTexplosion are assumed to behave as ideal gasThe equation ofstate specified for ideal gas can be expressed as follows

119901 = (120574 minus 1) 1205881198921198900 where 120574 =

119862119901

119862V 1198900= 119862V119879 (3)

where 120574 is the adiabatic exponent 120588119892is the density of the gas

1198900is the internal energy 119862

119901and 119862V are the specific heat at

constant pressure and volume respectively and 119879 is the gas


Table1Geometric

parametersa

ndsim

ulationresults

ofcompu

tatio

nalcases

considered

Case

number

SOD

Thickn

ess

Cellsize

Relativ

edensity

ofcore

Equivalent

solid

plate

thickn

ess

Peak

reflected

pressure

Maxim

ummom

entum

offro

ntface

Maxim

umdeflection

Failu

remod

e

119877 (mm)

Face

sheets

Core

Cell

wall

119897

(mm)

120588119888 ()

119905119904

(mm)

119901119903

(KPa)

119875

(kgtimes

ms)

Fron

tface

Back

face

Fron

tface

Back

face

119905119891

(mm)

119867119888

(mm)

119905119888

(mm)

120575119891

(mm)

120575119887

(mm)

mdashmdash

S20-1

3020

1732

1020

1035

579

53021times10

6546

mdash1619

Pitting

Pitting

S20-2

5020

1732

1020

1035

579

1300

0times10

6440

mdash1189

Pitting

Indenting

S20-3

8020

1732

1020

1035

579

29786times10

5284

760

377

Indenting

Mod

eIS20-4

100

20

1732

1020

1035

579

92518times10

4240

352

208

Indenting

Mod

eIS20-5

3020

1732

07

2074

8530

52770times10

6565

mdashmdash

Pitting

Pitting

S20-6

5020

1732

07

2074

8530

13002times10

6479

mdash1304

Pitting

Indenting

S20-7

8020

1732

07

2074

8530

29583times10

5312

1018

494

Indenting

Mod

eIS20-8

100

20

1732

07

2074

8530

92578times10

4274

411

267

Indenting

Mod

eIS20-9

3016

1732

1020

1035

500

47094times10

6495

mdashmdash

Pitting

Pitting

S20-10

5016

1732

1020

1035

500

12140times10

6460

mdash1354

Pitting

Indenting

S20-11

8016

1732

1020

1035

500

23078times10

5318

997

505

Indenting

Mod

eIS20-12

100

161732

1020

1035

500

85525times10

4246

509

281

Indenting

Mod

eIS20-13

3016

1732

07

2074

8450

46998times10

6518

mdashmdash

Pitting

Petalling

S20-14

5016

1732

07

2074

8450

12163times10

6495

mdash1576

Pitting

Indenting

S20-15

8016

1732

07

2074

8450

22944times10

5346

1285

678

Indenting

Mod

eIS20-16

100

161732

07

2074

8450

85567times10

4265

574

347

Indenting

Mod

eIS20-17

3012

1732

1020

1035

419

33315times10

6443

mdashmdash

Pitting

Petalling

S20-18

5012

1732

1020

1035

419

1000

4times10

6470

mdash1869

Pitting

Indenting

S20-19

8012

1732

1020

1035

419

21489times10

5345

1400

720

Indenting

Mod

eIS20-20

100

121732

1020

1035

419

83993times10

4283

771

427

Indenting

Mod

eIS20-21

3025

1732

1020

1035

679

55797times10

6554

mdashmdash

Pitting

Pitting

S20-22

5025

1732

1020

1035

679

13328times10

6423

2026

720

Indenting

Indenting

S20-23

8025

1732

1020

1035

679

30174times10

5290

547

278

Indenting

Mod

eIS20-24

100

25

1732

1020

1035

679

92833times10

4240

227

151

Mod

eIMod

eIS20-25

3020

1732

05

20546

495

52755times10

6597

mdashmdash

Pitting

Petalling

S20-26

5020

1732

05

20546

495

12955times10

6507

mdash1118

Pitting

Indenting

S20-27

8020

1732

05

20546

495

29245times10

5340

1174

583

Indenting

Mod

eIS20-28

100

20

1732

05

20546

495

89711times10

4305

615

383

Indenting

Mod

eIS28-1

3020

2425

1028

763

585

52730times10

6626

mdashmdash

Pitting

Pitting

S28-2

5020

2425

1028

763

585

12972times10

6542

mdash864

Pitting

Indenting

S28-3

8020

2425

1028

763

585

29478times10

5386

905

333

Indenting

Mod

eIS28-4

100

20

2425

1028

763

585

90553times10

4408

457

170

Indenting

Mod

eIS28-5

3020

2425

07

28546

532

52839times10

6585

mdashmdash

Pitting

Pitting

S28-6

5020

2425

07

28546

532

12950times10

6575

mdash1018

Pitting

Indenting

S28-7

8020

2425

07

28546

532

29364times10

5412

1115

456

Indenting

Mod

eIS28-8

100

20

2425

07

28546

532

90679times10

4327

516

240

Indenting

Mod

eI


Table1Con

tinued

Case

number

SOD

Thickn

ess

Cellsize

Relativ

edensity

ofcore

Equivalent

solid

plate

thickn

ess

Peak

reflected

pressure

Maxim

ummom

entum

offro

ntface

Maxim

umdeflection

Failu

remod

e

119877 (mm)

Face

sheets

Core

Cell

wall

119897

(mm)

120588119888 ()

119905119904

(mm)

119901119903

(KPa)

119875

(kgtimes

ms)

Fron

tface

Back

face

Fron

tface

Back

face

119905119891

(mm)

119867119888

(mm)

119905119888

(mm)

120575119891

(mm)

120575119887

(mm)

mdashmdash

S28-9

3016

2425

1028

763

505

47042times10

6587

mdashmdash

Pitting

Pitting

S28-10

5016

2425

1028

763

505

12155times10

6555

mdashmdash

Pitting

Pitting

S28-11

8016

2425

1028

763

505

23130times10

5409

1156

429

Indenting

Mod

eIS28-12

100

162425

1028

763

505

85910times10

4339

614

232

Indenting

Mod

eIS28-13

3016

2425

07

28546

452

47099times10

6619

mdashmdash

Pitting

Petalling

S28-14

5016

2425

07

28546

452

12130times10

6583

mdashmdash

Pitting

Pitting

S28-15

8016

2425

07

28546

452

23342times10

5435

1405

607

Indenting

Mod

eIS28-16

100

162425

07

28546

452

85914times10

4355

682

302

Indenting

Mod

eIS40-1

3020

3464

1040

546

589

52807times10

6714

mdashmdash

Pitting

Pitting

S40-2

5020

3464

1040

546

589

12993times10

6629

mdash77

9Pitting

Indenting

S40-3

8020

3464

1040

546

589

29633times10

5481

1120

270

Indenting

Mod

eIS40-4

100

20

3464

1040

546

589

91120times10

4408

620

144

Indenting

Mod

eIS40-5

3020

3464

07

40388

534

52818times10

674

1mdash

mdashPitting

Pitting

S40-6

5020

3464

07

40388

534

12993times10

6664

mdash614

Pitting

Indenting

S40-7

8020

3464

07

40388

534

29029times10

5504

1311

373

Indenting

Mod

eIS40-8

100

20

3464

07

40388

534

91133times10

4421

673

206

Indenting

Mod

eIS40-9

3016

3464

1040

546

509

46923times10

6686

mdashmdash

Pitting

Pitting

S40-10

5016

3464

1040

546

509

12123times10

6643

mdashmdash

Pitting

Pitting

S40-11

8016

3464

1040

546

509

23034times10

5493

1407

341

Indenting

Mod

eIS40-12

100

163464

1040

546

509

85560times10

4425

785

183

Indenting

Mod

eIS40-13

3016

3464

07

40388

454

47152times10

670

3mdash

mdashPitting

Pitting

S40-14

5016

3464

07

40388

454

12134times10

6665

mdashmdash

Pitting

Pitting

S40-15

8016

3464

07

40388

454

23274times10

5518

1659

482

Indenting

Mod

eIS40-16

100

163464

07

40388

454

85552times10

4438

846

263

Indenting

Mod

eI





119877

(mm)119905119904

(mm)119901119903

(KPa)119875

(kgtimesms)120575119904

(mm) mdash



120588

(kgm3)119864

(GPa) ] 119879119898

(K)119879119903

(K)119862

(JkgK)119860

(MPa)119861

(MPa) 119899 119888 1205760

119898

7900 200 03 1673 293 440 310 1000 065 007 100 100



0120588 and


119901 = 1198601015840

(1 minus

120596120588119890

11987711205880

) 119890minus1198771(1205880120588119890)

+ 1198611015840

(1 minus

120596120588119890

11987721205880

) 119890minus1198772(1205880120588119890)

+

120596120588119890

1205880

1198641198980

(4)


0are the density of




120588

(kgm3)119879

(K)119862

(JkgK) 1205741198900

(kJkg)1225 2882 7176 14 2068 times 105

1198601015840

1198611015840







120588

(kgm3)1198601015840

(GPa)1198611015840

(GPa) 1198771

1198772

120596



C-J pressure(kPa)

1630 37377 375 415 09 035 6930 60 times 106 21 times 107


TNT explosivePanel





Exponential decay

Time of arrival

times104

4

3

2

1

0

Pmax

000 005 010 015 020

Time (ms)

Pres

sure

(kPa

)


32 Validation





ak p

ress

ure (

kPa)



times104

4

3

2

1

0






(a)

(b)









Relative error()


(a) 119905 = 0 120583s (b) 119905 = 43 120583s (c) 119905 = 70 120583s

(d) 119905 = 121 120583s (e) 119905 = 270 120583s (f) 119905 = 454 120583s







Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(a) Front face

Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(b) Back face

Tearing failure


Stretching


4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(c) Corrugated core







Material failed

Defl

ectio

n (m

m)


35

30

25

15

20

10

5

00 20 40 60 80 100 120 140

(a)


Defl

ectio

n (m

m)


35

30

25

15

20

10

5

0

0 20 40 60 80 100 120 140

Material failed

(b)






Detonation point

Cylindrical charge


Gauge 2Gauge 1






Gauge 4Gauge 5

times106

6

5

4

3

2

1

0

000 001 002 003

Time (ms)

Pres

sure

(kPa

)

(a)

times106

6

5

4

3

2

1

0

Pres

sure

(kPa

)

000 001 002 003

Time (ms)


Gauge 4Gauge 5

(b)




5 Discussions





119891=





times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)



(b)




(a)


(b)


(c)


(d)


119891

= 20mm 119905c = 10mm and 119897 = 20mm (b) 119905119891

= 20mm 119905119888

= 10mm and 119897 = 28mm (c) 119905119891

= 20mm 119905119888

= 10mm and119897 = 40mm (d) 119905

119904

= 58mm


119888= 10mm 119897 = 20mm)





axim

um d

eflec

tion

(mm

)


Solid plate



Front face

Back face

35

100755025

30

25

20

10

5

0

15


119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm





119888=





times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



119888

= 10mm and 119897 =20mm







axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table1Geometric

parametersa

ndsim

ulationresults

ofcompu

tatio

nalcases

considered

Case

number

SOD

Thickn

ess

Cellsize

Relativ

edensity

ofcore

Equivalent

solid

plate

thickn

ess

Peak

reflected

pressure

Maxim

ummom

entum

offro

ntface

Maxim

umdeflection

Failu

remod

e

119877 (mm)

Face

sheets

Core

Cell

wall

119897

(mm)

120588119888 ()

119905119904

(mm)

119901119903

(KPa)

119875

(kgtimes

ms)

Fron

tface

Back

face

Fron

tface

Back

face

119905119891

(mm)

119867119888

(mm)

119905119888

(mm)

120575119891

(mm)

120575119887

(mm)

mdashmdash

S20-1

3020

1732

1020

1035

579

53021times10

6546

mdash1619

Pitting

Pitting

S20-2

5020

1732

1020

1035

579

1300

0times10

6440

mdash1189

Pitting

Indenting

S20-3

8020

1732

1020

1035

579

29786times10

5284

760

377

Indenting

Mod

eIS20-4

100

20

1732

1020

1035

579

92518times10

4240

352

208

Indenting

Mod

eIS20-5

3020

1732

07

2074

8530

52770times10

6565

mdashmdash

Pitting

Pitting

S20-6

5020

1732

07

2074

8530

13002times10

6479

mdash1304

Pitting

Indenting

S20-7

8020

1732

07

2074

8530

29583times10

5312

1018

494

Indenting

Mod

eIS20-8

100

20

1732

07

2074

8530

92578times10

4274

411

267

Indenting

Mod

eIS20-9

3016

1732

1020

1035

500

47094times10

6495

mdashmdash

Pitting

Pitting

S20-10

5016

1732

1020

1035

500

12140times10

6460

mdash1354

Pitting

Indenting

S20-11

8016

1732

1020

1035

500

23078times10

5318

997

505

Indenting

Mod

eIS20-12

100

161732

1020

1035

500

85525times10

4246

509

281

Indenting

Mod

eIS20-13

3016

1732

07

2074

8450

46998times10

6518

mdashmdash

Pitting

Petalling

S20-14

5016

1732

07

2074

8450

12163times10

6495

mdash1576

Pitting

Indenting

S20-15

8016

1732

07

2074

8450

22944times10

5346

1285

678

Indenting

Mod

eIS20-16

100

161732

07

2074

8450

85567times10

4265

574

347

Indenting

Mod

eIS20-17

3012

1732

1020

1035

419

33315times10

6443

mdashmdash

Pitting

Petalling

S20-18

5012

1732

1020

1035

419

1000

4times10

6470

mdash1869

Pitting

Indenting

S20-19

8012

1732

1020

1035

419

21489times10

5345

1400

720

Indenting

Mod

eIS20-20

100

121732

1020

1035

419

83993times10

4283

771

427

Indenting

Mod

eIS20-21

3025

1732

1020

1035

679

55797times10

6554

mdashmdash

Pitting

Pitting

S20-22

5025

1732

1020

1035

679

13328times10

6423

2026

720

Indenting

Indenting

S20-23

8025

1732

1020

1035

679

30174times10

5290

547

278

Indenting

Mod

eIS20-24

100

25

1732

1020

1035

679

92833times10

4240

227

151

Mod

eIMod

eIS20-25

3020

1732

05

20546

495

52755times10

6597

mdashmdash

Pitting

Petalling

S20-26

5020

1732

05

20546

495

12955times10

6507

mdash1118

Pitting

Indenting

S20-27

8020

1732

05

20546

495

29245times10

5340

1174

583

Indenting

Mod

eIS20-28

100

20

1732

05

20546

495

89711times10

4305

615

383

Indenting

Mod

eIS28-1

3020

2425

1028

763

585

52730times10

6626

mdashmdash

Pitting

Pitting

S28-2

5020

2425

1028

763

585

12972times10

6542

mdash864

Pitting

Indenting

S28-3

8020

2425

1028

763

585

29478times10

5386

905

333

Indenting

Mod

eIS28-4

100

20

2425

1028

763

585

90553times10

4408

457

170

Indenting

Mod

eIS28-5

3020

2425

07

28546

532

52839times10

6585

mdashmdash

Pitting

Pitting

S28-6

5020

2425

07

28546

532

12950times10

6575

mdash1018

Pitting

Indenting

S28-7

8020

2425

07

28546

532

29364times10

5412

1115

456

Indenting

Mod

eIS28-8

100

20

2425

07

28546

532

90679times10

4327

516

240

Indenting

Mod

eI


Table1Con

tinued

Case

number

SOD

Thickn

ess

Cellsize

Relativ

edensity

ofcore

Equivalent

solid

plate

thickn

ess

Peak

reflected

pressure

Maxim

ummom

entum

offro

ntface

Maxim

umdeflection

Failu

remod

e

119877 (mm)

Face

sheets

Core

Cell

wall

119897

(mm)

120588119888 ()

119905119904

(mm)

119901119903

(KPa)

119875

(kgtimes

ms)

Fron

tface

Back

face

Fron

tface

Back

face

119905119891

(mm)

119867119888

(mm)

119905119888

(mm)

120575119891

(mm)

120575119887

(mm)

mdashmdash

S28-9

3016

2425

1028

763

505

47042times10

6587

mdashmdash

Pitting

Pitting

S28-10

5016

2425

1028

763

505

12155times10

6555

mdashmdash

Pitting

Pitting

S28-11

8016

2425

1028

763

505

23130times10

5409

1156

429

Indenting

Mod

eIS28-12

100

162425

1028

763

505

85910times10

4339

614

232

Indenting

Mod

eIS28-13

3016

2425

07

28546

452

47099times10

6619

mdashmdash

Pitting

Petalling

S28-14

5016

2425

07

28546

452

12130times10

6583

mdashmdash

Pitting

Pitting

S28-15

8016

2425

07

28546

452

23342times10

5435

1405

607

Indenting

Mod

eIS28-16

100

162425

07

28546

452

85914times10

4355

682

302

Indenting

Mod

eIS40-1

3020

3464

1040

546

589

52807times10

6714

mdashmdash

Pitting

Pitting

S40-2

5020

3464

1040

546

589

12993times10

6629

mdash77

9Pitting

Indenting

S40-3

8020

3464

1040

546

589

29633times10

5481

1120

270

Indenting

Mod

eIS40-4

100

20

3464

1040

546

589

91120times10

4408

620

144

Indenting

Mod

eIS40-5

3020

3464

07

40388

534

52818times10

674

1mdash

mdashPitting

Pitting

S40-6

5020

3464

07

40388

534

12993times10

6664

mdash614

Pitting

Indenting

S40-7

8020

3464

07

40388

534

29029times10

5504

1311

373

Indenting

Mod

eIS40-8

100

20

3464

07

40388

534

91133times10

4421

673

206

Indenting

Mod

eIS40-9

3016

3464

1040

546

509

46923times10

6686

mdashmdash

Pitting

Pitting

S40-10

5016

3464

1040

546

509

12123times10

6643

mdashmdash

Pitting

Pitting

S40-11

8016

3464

1040

546

509

23034times10

5493

1407

341

Indenting

Mod

eIS40-12

100

163464

1040

546

509

85560times10

4425

785

183

Indenting

Mod

eIS40-13

3016

3464

07

40388

454

47152times10

670

3mdash

mdashPitting

Pitting

S40-14

5016

3464

07

40388

454

12134times10

6665

mdashmdash

Pitting

Pitting

S40-15

8016

3464

07

40388

454

23274times10

5518

1659

482

Indenting

Mod

eIS40-16

100

163464

07

40388

454

85552times10

4438

846

263

Indenting

Mod

eI





119877

(mm)119905119904

(mm)119901119903

(KPa)119875

(kgtimesms)120575119904

(mm) mdash



120588

(kgm3)119864

(GPa) ] 119879119898

(K)119879119903

(K)119862

(JkgK)119860

(MPa)119861

(MPa) 119899 119888 1205760

119898

7900 200 03 1673 293 440 310 1000 065 007 100 100



0120588 and


119901 = 1198601015840

(1 minus

120596120588119890

11987711205880

) 119890minus1198771(1205880120588119890)

+ 1198611015840

(1 minus

120596120588119890

11987721205880

) 119890minus1198772(1205880120588119890)

+

120596120588119890

1205880

1198641198980

(4)


0are the density of




120588

(kgm3)119879

(K)119862

(JkgK) 1205741198900

(kJkg)1225 2882 7176 14 2068 times 105

1198601015840

1198611015840







120588

(kgm3)1198601015840

(GPa)1198611015840

(GPa) 1198771

1198772

120596



C-J pressure(kPa)

1630 37377 375 415 09 035 6930 60 times 106 21 times 107


TNT explosivePanel





Exponential decay

Time of arrival

times104

4

3

2

1

0

Pmax

000 005 010 015 020

Time (ms)

Pres

sure

(kPa

)


32 Validation





ak p

ress

ure (

kPa)



times104

4

3

2

1

0






(a)

(b)









Relative error()


(a) 119905 = 0 120583s (b) 119905 = 43 120583s (c) 119905 = 70 120583s

(d) 119905 = 121 120583s (e) 119905 = 270 120583s (f) 119905 = 454 120583s







Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(a) Front face

Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(b) Back face

Tearing failure


Stretching


4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(c) Corrugated core







Material failed

Defl

ectio

n (m

m)


35

30

25

15

20

10

5

00 20 40 60 80 100 120 140

(a)


Defl

ectio

n (m

m)


35

30

25

15

20

10

5

0

0 20 40 60 80 100 120 140

Material failed

(b)






Detonation point

Cylindrical charge


Gauge 2Gauge 1






Gauge 4Gauge 5

times106

6

5

4

3

2

1

0

000 001 002 003

Time (ms)

Pres

sure

(kPa

)

(a)

times106

6

5

4

3

2

1

0

Pres

sure

(kPa

)

000 001 002 003

Time (ms)


Gauge 4Gauge 5

(b)




5 Discussions





119891=





times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)



(b)




(a)


(b)


(c)


(d)


119891

= 20mm 119905c = 10mm and 119897 = 20mm (b) 119905119891

= 20mm 119905119888

= 10mm and 119897 = 28mm (c) 119905119891

= 20mm 119905119888

= 10mm and119897 = 40mm (d) 119905

119904

= 58mm


119888= 10mm 119897 = 20mm)





axim

um d

eflec

tion

(mm

)


Solid plate



Front face

Back face

35

100755025

30

25

20

10

5

0

15


119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm





119888=





times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



119888

= 10mm and 119897 =20mm







axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table1Con

tinued

Case

number

SOD

Thickn

ess

Cellsize

Relativ

edensity

ofcore

Equivalent

solid

plate

thickn

ess

Peak

reflected

pressure

Maxim

ummom

entum

offro

ntface

Maxim

umdeflection

Failu

remod

e

119877 (mm)

Face

sheets

Core

Cell

wall

119897

(mm)

120588119888 ()

119905119904

(mm)

119901119903

(KPa)

119875

(kgtimes

ms)

Fron

tface

Back

face

Fron

tface

Back

face

119905119891

(mm)

119867119888

(mm)

119905119888

(mm)

120575119891

(mm)

120575119887

(mm)

mdashmdash

S28-9

3016

2425

1028

763

505

47042times10

6587

mdashmdash

Pitting

Pitting

S28-10

5016

2425

1028

763

505

12155times10

6555

mdashmdash

Pitting

Pitting

S28-11

8016

2425

1028

763

505

23130times10

5409

1156

429

Indenting

Mod

eIS28-12

100

162425

1028

763

505

85910times10

4339

614

232

Indenting

Mod

eIS28-13

3016

2425

07

28546

452

47099times10

6619

mdashmdash

Pitting

Petalling

S28-14

5016

2425

07

28546

452

12130times10

6583

mdashmdash

Pitting

Pitting

S28-15

8016

2425

07

28546

452

23342times10

5435

1405

607

Indenting

Mod

eIS28-16

100

162425

07

28546

452

85914times10

4355

682

302

Indenting

Mod

eIS40-1

3020

3464

1040

546

589

52807times10

6714

mdashmdash

Pitting

Pitting

S40-2

5020

3464

1040

546

589

12993times10

6629

mdash77

9Pitting

Indenting

S40-3

8020

3464

1040

546

589

29633times10

5481

1120

270

Indenting

Mod

eIS40-4

100

20

3464

1040

546

589

91120times10

4408

620

144

Indenting

Mod

eIS40-5

3020

3464

07

40388

534

52818times10

674

1mdash

mdashPitting

Pitting

S40-6

5020

3464

07

40388

534

12993times10

6664

mdash614

Pitting

Indenting

S40-7

8020

3464

07

40388

534

29029times10

5504

1311

373

Indenting

Mod

eIS40-8

100

20

3464

07

40388

534

91133times10

4421

673

206

Indenting

Mod

eIS40-9

3016

3464

1040

546

509

46923times10

6686

mdashmdash

Pitting

Pitting

S40-10

5016

3464

1040

546

509

12123times10

6643

mdashmdash

Pitting

Pitting

S40-11

8016

3464

1040

546

509

23034times10

5493

1407

341

Indenting

Mod

eIS40-12

100

163464

1040

546

509

85560times10

4425

785

183

Indenting

Mod

eIS40-13

3016

3464

07

40388

454

47152times10

670

3mdash

mdashPitting

Pitting

S40-14

5016

3464

07

40388

454

12134times10

6665

mdashmdash

Pitting

Pitting

S40-15

8016

3464

07

40388

454

23274times10

5518

1659

482

Indenting

Mod

eIS40-16

100

163464

07

40388

454

85552times10

4438

846

263

Indenting

Mod

eI





119877

(mm)119905119904

(mm)119901119903

(KPa)119875

(kgtimesms)120575119904

(mm) mdash



120588

(kgm3)119864

(GPa) ] 119879119898

(K)119879119903

(K)119862

(JkgK)119860

(MPa)119861

(MPa) 119899 119888 1205760

119898

7900 200 03 1673 293 440 310 1000 065 007 100 100



0120588 and


119901 = 1198601015840

(1 minus

120596120588119890

11987711205880

) 119890minus1198771(1205880120588119890)

+ 1198611015840

(1 minus

120596120588119890

11987721205880

) 119890minus1198772(1205880120588119890)

+

120596120588119890

1205880

1198641198980

(4)


0are the density of




120588

(kgm3)119879

(K)119862

(JkgK) 1205741198900

(kJkg)1225 2882 7176 14 2068 times 105

1198601015840

1198611015840







120588

(kgm3)1198601015840

(GPa)1198611015840

(GPa) 1198771

1198772

120596



C-J pressure(kPa)

1630 37377 375 415 09 035 6930 60 times 106 21 times 107


TNT explosivePanel





Exponential decay

Time of arrival

times104

4

3

2

1

0

Pmax

000 005 010 015 020

Time (ms)

Pres

sure

(kPa

)


32 Validation





ak p

ress

ure (

kPa)



times104

4

3

2

1

0






(a)

(b)









Relative error()


(a) 119905 = 0 120583s (b) 119905 = 43 120583s (c) 119905 = 70 120583s

(d) 119905 = 121 120583s (e) 119905 = 270 120583s (f) 119905 = 454 120583s







Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(a) Front face

Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(b) Back face

Tearing failure


Stretching


4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(c) Corrugated core







Material failed

Defl

ectio

n (m

m)


35

30

25

15

20

10

5

00 20 40 60 80 100 120 140

(a)


Defl

ectio

n (m

m)


35

30

25

15

20

10

5

0

0 20 40 60 80 100 120 140

Material failed

(b)






Detonation point

Cylindrical charge


Gauge 2Gauge 1






Gauge 4Gauge 5

times106

6

5

4

3

2

1

0

000 001 002 003

Time (ms)

Pres

sure

(kPa

)

(a)

times106

6

5

4

3

2

1

0

Pres

sure

(kPa

)

000 001 002 003

Time (ms)


Gauge 4Gauge 5

(b)




5 Discussions





119891=





times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)



(b)




(a)


(b)


(c)


(d)


119891

= 20mm 119905c = 10mm and 119897 = 20mm (b) 119905119891

= 20mm 119905119888

= 10mm and 119897 = 28mm (c) 119905119891

= 20mm 119905119888

= 10mm and119897 = 40mm (d) 119905

119904

= 58mm


119888= 10mm 119897 = 20mm)





axim

um d

eflec

tion

(mm

)


Solid plate



Front face

Back face

35

100755025

30

25

20

10

5

0

15


119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm





119888=





times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



119888

= 10mm and 119897 =20mm







axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119877

(mm)119905119904

(mm)119901119903

(KPa)119875

(kgtimesms)120575119904

(mm) mdash



120588

(kgm3)119864

(GPa) ] 119879119898

(K)119879119903

(K)119862

(JkgK)119860

(MPa)119861

(MPa) 119899 119888 1205760

119898

7900 200 03 1673 293 440 310 1000 065 007 100 100



0120588 and


119901 = 1198601015840

(1 minus

120596120588119890

11987711205880

) 119890minus1198771(1205880120588119890)

+ 1198611015840

(1 minus

120596120588119890

11987721205880

) 119890minus1198772(1205880120588119890)

+

120596120588119890

1205880

1198641198980

(4)


0are the density of




120588

(kgm3)119879

(K)119862

(JkgK) 1205741198900

(kJkg)1225 2882 7176 14 2068 times 105

1198601015840

1198611015840







120588

(kgm3)1198601015840

(GPa)1198611015840

(GPa) 1198771

1198772

120596



C-J pressure(kPa)

1630 37377 375 415 09 035 6930 60 times 106 21 times 107


TNT explosivePanel





Exponential decay

Time of arrival

times104

4

3

2

1

0

Pmax

000 005 010 015 020

Time (ms)

Pres

sure

(kPa

)


32 Validation





ak p

ress

ure (

kPa)



times104

4

3

2

1

0






(a)

(b)









Relative error()


(a) 119905 = 0 120583s (b) 119905 = 43 120583s (c) 119905 = 70 120583s

(d) 119905 = 121 120583s (e) 119905 = 270 120583s (f) 119905 = 454 120583s







Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(a) Front face

Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(b) Back face

Tearing failure


Stretching


4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(c) Corrugated core







Material failed

Defl

ectio

n (m

m)


35

30

25

15

20

10

5

00 20 40 60 80 100 120 140

(a)


Defl

ectio

n (m

m)


35

30

25

15

20

10

5

0

0 20 40 60 80 100 120 140

Material failed

(b)






Detonation point

Cylindrical charge


Gauge 2Gauge 1






Gauge 4Gauge 5

times106

6

5

4

3

2

1

0

000 001 002 003

Time (ms)

Pres

sure

(kPa

)

(a)

times106

6

5

4

3

2

1

0

Pres

sure

(kPa

)

000 001 002 003

Time (ms)


Gauge 4Gauge 5

(b)




5 Discussions





119891=





times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)



(b)




(a)


(b)


(c)


(d)


119891

= 20mm 119905c = 10mm and 119897 = 20mm (b) 119905119891

= 20mm 119905119888

= 10mm and 119897 = 28mm (c) 119905119891

= 20mm 119905119888

= 10mm and119897 = 40mm (d) 119905

119904

= 58mm


119888= 10mm 119897 = 20mm)





axim

um d

eflec

tion

(mm

)


Solid plate



Front face

Back face

35

100755025

30

25

20

10

5

0

15


119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm





119888=





times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



119888

= 10mm and 119897 =20mm







axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120588

(kgm3)1198601015840

(GPa)1198611015840

(GPa) 1198771

1198772

120596



C-J pressure(kPa)

1630 37377 375 415 09 035 6930 60 times 106 21 times 107


TNT explosivePanel





Exponential decay

Time of arrival

times104

4

3

2

1

0

Pmax

000 005 010 015 020

Time (ms)

Pres

sure

(kPa

)


32 Validation





ak p

ress

ure (

kPa)



times104

4

3

2

1

0






(a)

(b)









Relative error()


(a) 119905 = 0 120583s (b) 119905 = 43 120583s (c) 119905 = 70 120583s

(d) 119905 = 121 120583s (e) 119905 = 270 120583s (f) 119905 = 454 120583s







Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(a) Front face

Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(b) Back face

Tearing failure


Stretching


4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(c) Corrugated core







Material failed

Defl

ectio

n (m

m)


35

30

25

15

20

10

5

00 20 40 60 80 100 120 140

(a)


Defl

ectio

n (m

m)


35

30

25

15

20

10

5

0

0 20 40 60 80 100 120 140

Material failed

(b)






Detonation point

Cylindrical charge


Gauge 2Gauge 1






Gauge 4Gauge 5

times106

6

5

4

3

2

1

0

000 001 002 003

Time (ms)

Pres

sure

(kPa

)

(a)

times106

6

5

4

3

2

1

0

Pres

sure

(kPa

)

000 001 002 003

Time (ms)


Gauge 4Gauge 5

(b)




5 Discussions





119891=





times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)



(b)




(a)


(b)


(c)


(d)


119891

= 20mm 119905c = 10mm and 119897 = 20mm (b) 119905119891

= 20mm 119905119888

= 10mm and 119897 = 28mm (c) 119905119891

= 20mm 119905119888

= 10mm and119897 = 40mm (d) 119905

119904

= 58mm


119888= 10mm 119897 = 20mm)





axim

um d

eflec

tion

(mm

)


Solid plate



Front face

Back face

35

100755025

30

25

20

10

5

0

15


119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm





119888=





times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



119888

= 10mm and 119897 =20mm







axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










ak p

ress

ure (

kPa)



times104

4

3

2

1

0






(a)

(b)









Relative error()


(a) 119905 = 0 120583s (b) 119905 = 43 120583s (c) 119905 = 70 120583s

(d) 119905 = 121 120583s (e) 119905 = 270 120583s (f) 119905 = 454 120583s







Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(a) Front face

Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(b) Back face

Tearing failure


Stretching


4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(c) Corrugated core







Material failed

Defl

ectio

n (m

m)


35

30

25

15

20

10

5

00 20 40 60 80 100 120 140

(a)


Defl

ectio

n (m

m)


35

30

25

15

20

10

5

0

0 20 40 60 80 100 120 140

Material failed

(b)






Detonation point

Cylindrical charge


Gauge 2Gauge 1






Gauge 4Gauge 5

times106

6

5

4

3

2

1

0

000 001 002 003

Time (ms)

Pres

sure

(kPa

)

(a)

times106

6

5

4

3

2

1

0

Pres

sure

(kPa

)

000 001 002 003

Time (ms)


Gauge 4Gauge 5

(b)




5 Discussions





119891=





times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)



(b)




(a)


(b)


(c)


(d)


119891

= 20mm 119905c = 10mm and 119897 = 20mm (b) 119905119891

= 20mm 119905119888

= 10mm and 119897 = 28mm (c) 119905119891

= 20mm 119905119888

= 10mm and119897 = 40mm (d) 119905

119904

= 58mm


119888= 10mm 119897 = 20mm)





axim

um d

eflec

tion

(mm

)


Solid plate



Front face

Back face

35

100755025

30

25

20

10

5

0

15


119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm





119888=





times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



119888

= 10mm and 119897 =20mm







axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Relative error()


(a) 119905 = 0 120583s (b) 119905 = 43 120583s (c) 119905 = 70 120583s

(d) 119905 = 121 120583s (e) 119905 = 270 120583s (f) 119905 = 454 120583s







Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(a) Front face

Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(b) Back face

Tearing failure


Stretching


4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(c) Corrugated core







Material failed

Defl

ectio

n (m

m)


35

30

25

15

20

10

5

00 20 40 60 80 100 120 140

(a)


Defl

ectio

n (m

m)


35

30

25

15

20

10

5

0

0 20 40 60 80 100 120 140

Material failed

(b)






Detonation point

Cylindrical charge


Gauge 2Gauge 1






Gauge 4Gauge 5

times106

6

5

4

3

2

1

0

000 001 002 003

Time (ms)

Pres

sure

(kPa

)

(a)

times106

6

5

4

3

2

1

0

Pres

sure

(kPa

)

000 001 002 003

Time (ms)


Gauge 4Gauge 5

(b)




5 Discussions





119891=





times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)



(b)




(a)


(b)


(c)


(d)


119891

= 20mm 119905c = 10mm and 119897 = 20mm (b) 119905119891

= 20mm 119905119888

= 10mm and 119897 = 28mm (c) 119905119891

= 20mm 119905119888

= 10mm and119897 = 40mm (d) 119905

119904

= 58mm


119888= 10mm 119897 = 20mm)





axim

um d

eflec

tion

(mm

)


Solid plate



Front face

Back face

35

100755025

30

25

20

10

5

0

15


119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm





119888=





times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



119888

= 10mm and 119897 =20mm







axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(a) Front face

Tearing failure

4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(b) Back face

Tearing failure


Stretching


4200e minus 01

3780e minus 01

3360e minus 01

2940e minus 01

2520e minus 01

2100e minus 01

1680e minus 01

1260e minus 01

8400e minus 02

4200e minus 02

0000e + 00

EFFPLSTN [All]

(c) Corrugated core







Material failed

Defl

ectio

n (m

m)


35

30

25

15

20

10

5

00 20 40 60 80 100 120 140

(a)


Defl

ectio

n (m

m)


35

30

25

15

20

10

5

0

0 20 40 60 80 100 120 140

Material failed

(b)






Detonation point

Cylindrical charge


Gauge 2Gauge 1






Gauge 4Gauge 5

times106

6

5

4

3

2

1

0

000 001 002 003

Time (ms)

Pres

sure

(kPa

)

(a)

times106

6

5

4

3

2

1

0

Pres

sure

(kPa

)

000 001 002 003

Time (ms)


Gauge 4Gauge 5

(b)




5 Discussions





119891=





times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)



(b)




(a)


(b)


(c)


(d)


119891

= 20mm 119905c = 10mm and 119897 = 20mm (b) 119905119891

= 20mm 119905119888

= 10mm and 119897 = 28mm (c) 119905119891

= 20mm 119905119888

= 10mm and119897 = 40mm (d) 119905

119904

= 58mm


119888= 10mm 119897 = 20mm)





axim

um d

eflec

tion

(mm

)


Solid plate



Front face

Back face

35

100755025

30

25

20

10

5

0

15


119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm





119888=





times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



119888

= 10mm and 119897 =20mm







axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Material failed

Defl

ectio

n (m

m)


35

30

25

15

20

10

5

00 20 40 60 80 100 120 140

(a)


Defl

ectio

n (m

m)


35

30

25

15

20

10

5

0

0 20 40 60 80 100 120 140

Material failed

(b)






Detonation point

Cylindrical charge


Gauge 2Gauge 1






Gauge 4Gauge 5

times106

6

5

4

3

2

1

0

000 001 002 003

Time (ms)

Pres

sure

(kPa

)

(a)

times106

6

5

4

3

2

1

0

Pres

sure

(kPa

)

000 001 002 003

Time (ms)


Gauge 4Gauge 5

(b)




5 Discussions





119891=





times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)



(b)




(a)


(b)


(c)


(d)


119891

= 20mm 119905c = 10mm and 119897 = 20mm (b) 119905119891

= 20mm 119905119888

= 10mm and 119897 = 28mm (c) 119905119891

= 20mm 119905119888

= 10mm and119897 = 40mm (d) 119905

119904

= 58mm


119888= 10mm 119897 = 20mm)





axim

um d

eflec

tion

(mm

)


Solid plate



Front face

Back face

35

100755025

30

25

20

10

5

0

15


119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm





119888=





times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



119888

= 10mm and 119897 =20mm







axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Gauge 4Gauge 5

times106

6

5

4

3

2

1

0

000 001 002 003

Time (ms)

Pres

sure

(kPa

)

(a)

times106

6

5

4

3

2

1

0

Pres

sure

(kPa

)

000 001 002 003

Time (ms)


Gauge 4Gauge 5

(b)




5 Discussions





119891=





times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)



(b)




(a)


(b)


(c)


(d)


119891

= 20mm 119905c = 10mm and 119897 = 20mm (b) 119905119891

= 20mm 119905119888

= 10mm and 119897 = 28mm (c) 119905119891

= 20mm 119905119888

= 10mm and119897 = 40mm (d) 119905

119904

= 58mm


119888= 10mm 119897 = 20mm)





axim

um d

eflec

tion

(mm

)


Solid plate



Front face

Back face

35

100755025

30

25

20

10

5

0

15


119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm





119888=





times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



119888

= 10mm and 119897 =20mm







axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)



(b)




(a)


(b)


(c)


(d)


119891

= 20mm 119905c = 10mm and 119897 = 20mm (b) 119905119891

= 20mm 119905119888

= 10mm and 119897 = 28mm (c) 119905119891

= 20mm 119905119888

= 10mm and119897 = 40mm (d) 119905

119904

= 58mm


119888= 10mm 119897 = 20mm)





axim

um d

eflec

tion

(mm

)


Solid plate



Front face

Back face

35

100755025

30

25

20

10

5

0

15


119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm





119888=





times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



119888

= 10mm and 119897 =20mm







axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










axim

um d

eflec

tion

(mm

)


Solid plate



Front face

Back face

35

100755025

30

25

20

10

5

0

15


119891

= 20mm 119905119888

= 10mm 119905119904

= 58mm





119888=





times106

2

1

48 49 50 51 52 53

Peak

refle

cted

pre

ssur

e (kP

a) Enlarged view


Enlarged field

times106

6

7

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



119888

= 10mm and 119897 =20mm







axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










axim

um d

eflec

tion

(mm

)

30

25

20

15

10

5

025 50 75 100





119888

= 10mm 119897 = 20mm)




times106

6

5

4

3

2

1

0

25 50 75 100


Peak

refle

cted

pre

ssur

e (kP

a)


(a)

times106

6

5

4

3

2

1

0

Peak

refle

cted

pre

ssur

e (kP

a)

25 50 75 100



(b)





25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










25

20

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)



Back face


30

20

25

15

10

5

025 50 75 100


Max

imum

defl

ectio

n (m

m)




6 Conclusions


120588c = 1035

120588c = 763

120588c = 546

20

15

10

5

0

25 50 75 100


Max

imum

defl

ectio

n (m

m)






Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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