mixed numerical and experimental methods applied to...

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 1/29

S. Turcaud†, L. Guiducci†, P. Fratzl†, Y. J. M. Bréchet ‡, and J. W. C. Dunlop†

† Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Potsdam, Germany. ‡ SIMAP, Grenoble Institute of Technology, France

Mixed numerical and experimental methodsapplied to the mechanical characterization

of bio-based materials

Some design principles of biomimetic actuators

Thematic workshop

April 27-28, 2011Vila Real, Portugal

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 2/29

Bio-inspiration

Structural BiologyPhysiology…

Structure –Function Relations

We see the solution and need tofind the problem which was solved

MaterialsSciences

EngineeringDesign

We know the problem and need a solution

Introduction: Biomimetics

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 3/29

Biological Material vs Engineering Material

Few Chemical Elements dominate:C, N, O, H, Ca, P, Si, S….

Large Variety of Elements:Fe, Cr, Ni, Al, Si, C, N, O, …

Growthby biologically controlled

self-assembly (approximate design)

Fabricationfrom melts, powders, solutions,

etc. (exact design)

Adaptation of form and structure

to the function

Design of the part and Selection of material according to function

Modeling and Remodeling: Capability of adaptation to changing environmental conditions.

Secure Designof the part and

secure materials selection (considering possible

maximum loads as well as fatigue)

Healing: Capability of self-repair

Hierarchical Structureat all size levels

Form (of the part) and Micro-structure (of the material)

[Fratzl - J. Roy. Soc. Int. 2007]

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 4/29

Orientation of cellulose microfibrils in the scales of the pine cone

[Dawson et al. - Nature 2007]

Swelling and shrinking of fibre-reinforced matrix polymers

Pine cones: opening while drying

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 5/29

Wheat awns: a humidity driven motor

Night Day Night

[Elbaum et al. – Science 2007]

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 6/29

[Fratzl et al. – Faraday Discussions 2007]

Microfibrils angle control swelling at the cell level

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 7/29

Ice plant: A geometric-controlled opening

Hygroscopic keel

top-view of dry capsule top-view of wet capsule

swelling of individual cells

Wetting

[Harrington, M. – Guiducci, L. - Razghandi, K.]

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 8/29

[Rivka Elbaum, Yael Abraham, University of Jerusalem Israel]

Helical actuation of Erodium awns upon drying

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 9/29

General mechanical formulation

X xx = Φ(X)

initial geometry final geometry

)()( * xxel εεε +=

)(: xE elεσ =

)(* Xεeigenstrain

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 10/29

Bilayer Top-Down Analogy

Δ Relativehumidity

[Davide Ruffoni, Thomas Antretter]

Biological system

[Timoshenko - 1925]

r

h/2

Simple model

h

hrε

∝1

elastic material (E, ν)Passive ε=0Active ε=1

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 11/29

Cuboid shapes

Finite Element ModelGeometry

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 12/29

Cuboid partitions

Finite Element ModelArchitecture

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 13/29

Graphical picking Helical distributionRandom assignation

Finite Element ModelEigenstrain field

Passive ε=0Active ε=1

elastic material (E=1, ν=0.3)

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 14/29

ABAQUS©

Finite Element ModelHelical Actuation

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 15/29

ActivePassive

Controlling global actuation through material distribution

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 16/29

[An excursion into the design space of biomimetic architectured biphasic actuatorsTurcaud, S. – Guiducci, L. – Fratzl, P. – Bréchet, Y – Dunlop, J. - IJMR 2011]

symmetrical locking

rotational axis

nothing

mirror plane

Extrudable cross-sections

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R1 1M R4 0M

Restricting the space of actuation

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Finite element model

Point-Spring model

Biology

)(:: *εεεσ −== EE el

)( 0llkkxf −−=−=

Frameworks for eigenstrain actuation

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 19/29

Bending

r

)1(0 ε+l

2.0=ε

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 20/29

Twisting

θ

)1(0 ε+l

2.0=ε

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 21/29

Curling = Bending + Twisting

)1(0 Bl ε+

)1(0 Tl ε+

2.0|2.0 == TB εε

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 22/29

Exploring parameter space

04.0

==

T

B

εε

4.00

==

T

B

εε

4.04.0

==

T

B

εε

2.06.0

==

T

B

εε

00

==

T

B

εε

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 23/29

Space Curve

Frenet-Serret Framet

nb ntb

dsstd

kn

dssPdt

∧=

=

=

)(1

)(

P(s)

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛∧

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

bnt

kbnt

dsd 0

τ )(skcurvature

)(sτtorsion

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 24/29

Curvature

Bε

k

00

==

τεT

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 25/29

Tε

τ

Torsion

1.0=Bε

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 26/29

Tε

k

Coupling

1.0=Bε

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 27/29

Spatial functions

0>=

aasBε

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 28/29

Conclusion

Biological passive hygroscopic actuators

MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES | Sébastien Turcaud, Department of Biomaterials Page 29/29

MPIKG – Berlin, GermanyPeter Fratzl, John Dunlop, Ingo Burgert, Matt Harington, Lorenzo Guiducci, Khashayar Razghandi

SIMAP – Grenoble, FranceYves Bréchet

Acknowledgments

University of Jerusalem, IsraelRivka Elbaum, Yael Abraham