continuum damage mechanics of geomaterials at finite strain
DESCRIPTION
Continuum damage mechanics of geomaterials at finite strain. MDU. A. Karrech, Research Scientist, CSIRO K. Regenauer-Lieb, T. Poulet, P. Schaubs, Y, Zhang 29 September 2010. Outline. 1 Background Motivation Current approach 2 Elasto-visco-plasticity at finite strain - PowerPoint PPT PresentationTRANSCRIPT
Continuum damage mechanics ofgeomaterials at finite strain
A. Karrech, Research Scientist, CSIRO
K. Regenauer-Lieb, T. Poulet, P. Schaubs, Y, Zhang
29 September 2010
MDU
Outline
1 BackgroundMotivationCurrent approach
2 Elasto-visco-plasticity at finite strain
Multiplicative decompositionConstitutive relations
3 Damage mechanismVoid growth under several control mechanismsThe limit theory approximation
4 Validation / ApplicationValidation of the large transformations modelDamage of a notched plate and effects of pressureChemo-thermo-hydro-mechanics (See Thomas Poulet) Damage down under (See Peter Schaubs)
5 Summary
Damage at Finite Strain
Instabilities
Large transformations to describe earth systems instabilities
Damage at Finite Strain
Material Softening
•The predicted forces for splitting continents apart are much higher then available from plate tectonics.
•Time and length scales can’t be achieved in the laboratory.
Regenauer-Lieb et al 06, Nature
Outline
1 BackgroundMotivationCurrent approach
2 Elasto-visco-plasticity at finite strain
Multiplicative decompositionConstitutive relations
3 Damage mechanismVoid growth under several control mechanismsThe limit theory approximation
4 Validation / ApplicationValidation of the large transformations modelDamage of a notched plate and effects of pressureChemo-thermo-hydro-mechanics (See Thomas Poulet) Damage down under (See Peter Schaubs)
5 Summary
Finite strain -- Review
• Additive strain rate decomposition (similar to small deformations): Green Naghdi(65), Mandel (72) , Nemat-Nasser (81)...
• Multiplicative gradient decomposition: Lee and Liu(67), Lee (69)
• Numerical integration: Simo et al. (80s-94), Argyris and Doltsinis(80s), Miehe(90s)
• Several inconsistencies (aberrant oscillations observed by Dienes (79) Simo and Pister (82), K. Regenauer-Lieb and H. Mulhaus (06)…)
• Logarithmic corotational rates: Xiao, Buhrns Meyers (98-06)
• Metallic materials: Lin, Brocks, Betten (02,04,06)
• Formulation + numerical integration for geomaterials: current work
Finite strain – Basic concept
0TT and 1,udu • Small perturbations:
• (+) Well understood + Easy integration
• (-) Limitations in predicting instabilities
Large transformations: 0TT and 1,udu
Finite strain – Oscillations
Source of the figure: www.wikepidia.com
How to formulate thermo-mechanical coupled models for frictional materials in finite strain
How to overcome thesespurious oscillations?
Decomposition
eT
eT
XX
X
X
X
XF
The deformation gradient is:
Hence, the multiplicative decomposition:
FFFFFF ThevpThˆ
XF
ˆ
We consider the measure of athermal strain:
)(Ln2
1 and )(Ln
2
1)(Ln
2
1 et bhFFbh
Objective rates
Objective rates
Dissipation inequality
Helmholtz F. E. and dissipation
Helmholtz F. E. and dissipation
Principle of maximum dissipation
Outline
1 BackgroundMotivationCurrent approach
2 Elasto-visco-plasticity at finite strain
Multiplicative decompositionConstitutive relations
3 Damage mechanismVoid growth under several control mechanismsThe limit theory approximation
4 Validation / ApplicationValidation of the large transformations modelDamage of a notched plate and effects of pressureChemo-thermo-hydro-mechanics (See Thomas Poulet) Damage down under (See Peter Schaubs)
5 Summary
Micro-scale model
A. C. F. Cocks and M. F. Ashby, progress in materials science, 1982, Vol. 27, pp. 189 to 244
Comparison with other damage models
1 ),f1()f1(f For small f,
Cocks and Ashby models coincide with the descriptions of Kachanov (58) and Lemaitre and chaboche (80s)
f1
1Yf
dt
df0
The comparison highlights what we believe to be certain fundamental weaknesses of the continuum equations:
first, the prediction that the damage-rate is finite even when there is nodamage;
second, the prediction that the damage-rate always accelerates with damage;
Current approach
Assumptions:
• Vacancies within a given RVE are assumed to be within a spacing of min(2d, 2L),
(d and L are distances in the longitudinal and radial directions)
• Voids are assumed to be of small size as compared to the
• Voids are self-similar in terms of shape during the deformation process.
Upper limit (MARTIN, JMPS, 62)
V
ddVWW "'.)'()"( * uTσε
Current approach
After Integration (Karrech el al., ICAMEM Conference 2010)
inng DDD )1()1(
Similarly to Dahar et al (1996), we add a nucleation effect (no justification yet)
1)()1( }1{ YDD n
Integration with respect to the thermodynamic force of damage:
c)Y(Y1)D1(f }1n{D
Outline
1 BackgroundMotivationCurrent approach
2 Elasto-visco-plasticity at finite strain
Multiplicative decompositionConstitutive relations
3 Damage mechanismVoid growth under several control mechanismsThe limit theory approximation
4 Validation / ApplicationValidation of the large transformations modelDamage of a notched plate and effects of pressureChemo-thermo-hydro-mechanics (See Thomas Poulet) Damage down under (See Peter Schaubs)
5 Summary
Axially loaded sample
Axially loaded sample
Simple Shear
Simple Shear in hyer-elasto-plasticity
Necking problem
Good agreement between the experimental and numerical results
Triaxial test
Damage of a notched plate (Olivine)
Effect of pressure dependency
Effect of pressure dependency
Courtesy of Arcady Dyskin, UWA
Outline
1 BackgroundMotivationCurrent approach
2 Elasto-visco-plasticity at finite strain
Multiplicative decompositionConstitutive relations
3 Damage mechanismVoid growth under several control mechanismsThe limit theory approximation
4 Validation / ApplicationValidation of the large transformations modelDamage of a notched plate and effects of pressureChemo-thermo-hydro-mechanics (See Thomas Poulet) Damage down under (See Peter Schaubs)
5 Summary
Chemo-thermo-hydro-mechanics
(d) ...2,1 rqc.vc
(c) rqbpM
1
(b) rqT.vCTC
(a) 0bp
i,ii,i
ffi,i
TTi,iii
fp
fp
i,'
j,ij
Chemo-thermo-hydro-mechanics
(d) cq
(c) pq
(b) kTq
(a) uu2
1 with C
i,i
i,f
fi
i,Ti
i,jj,iijepijkl
'ij
Permeability evolution with damage
Chemo-thermo-hydro-mechanics
Fluid flow through damaged zones
Preliminary chemistry
Invitation
I invite you to talk to Thomas Poulet for more details about multi-physics Problems
Outline
1 BackgroundMotivationCurrent approach
2 Elasto-visco-plasticity at finite strain
Multiplicative decompositionConstitutive relations
3 Damage mechanismVoid growth under several control mechanismsThe limit theory approximation
4 Validation / ApplicationValidation of the large transformations modelDamage of a notched plate and effects of pressureChemo-thermo-hydro-mechanics (See Thomas Poulet) Damage down under (See Peter Schaubs)
5 Summary
Damage & thermo-coupling
• The Late Archaean Yilgarn Craton of Western Australia hosting orogenic gold deposits
• Different loading scenarios
Invitation
I invite you to talk to Peter Schaubs for more details about the field application
Outline
1 BackgroundMotivationCurrent approach
2 Elasto-visco-plasticity at finite strain
Multiplicative decompositionConstitutive relations
3 Damage mechanismVoid growth under several control mechanismsThe limit theory approximation
4 Validation / ApplicationValidation of the large transformations modelDamage of a notched plate and effects of pressureChemo-thermo-hydro-mechanics (See Thomas Poulet) Damage down under (See Peter Schaubs)
5 Conclusions
Outline
• Finite strain for geo-materials based on logarithmic strain measures and corotational rates.
• Solution for the spurious oscillations
• Continuum damage mechanics following based on approximate potential
• Instabilities and localizations are accelerated in such circumstances
• Multi-physics problems in the context of mining
Thank you
Computational Geoscience GroupDr Ali KarrechResearch Scientist @ CSIROAdjunct Associate Professor @ UWA
Phone: +61 8 64 36 86 96 Email: [email protected]: www.csiro.au