mixed numerical and experimental methods applied to...
TRANSCRIPT
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
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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]
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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
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Wheat awns: a humidity driven motor
Night Day Night
[Elbaum et al. – Science 2007]
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[Fratzl et al. – Faraday Discussions 2007]
Microfibrils angle control swelling at the cell level
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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
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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
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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
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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
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Tε
k
Coupling
1.0=Bε
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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