1. Stress induced instabilities in material science and biology
C. Misbah, CNRS and Univ. J. Fourier Grenoble I
Los Angeles October. 2005
Oct. 18th 2005
IPAM Oct. 2005

2. Uniaxial stress
Biaxial stress
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3. Questions 1) Front growth or recession? Solid 2) Planar front stable?
Melt, vapor
1) Front growth or
recession?
Solid
2) Planar front stable?
Solid
3) Ultimate stage?
Oct. 18th 2005
IPAM Oct. 2005

4. time Coarsening or fixed ? Stranski-Krastanov? Size selection?
Perpetual coarsening?
Oct. 18th 2005
IPAM Oct. 2005

5. ATG Intability (Asaro-Tiller,1972 -Grinfeld, 1986)
Quantum dots formation
pyramid-shaped quantum dots grown
from indium, gallium, and arsenic.
Each dot is about 20 nanometers
wide and 8 nanometers in height.
Oct. 18th 2005
IPAM Oct. 2005

6. Swelling or shrinkage of gels
Clamped at bottom
Gel swelling
T. Tanaka, H. Tanaka,
Kawasaki, Sekimoto, Onuki
Oct. 18th 2005
IPAM Oct. 2005

7. Misbah C., Renard F., Gratier J.P., Kassner K.,
Geoph. Res. Lett., 31, L6618 (2004).
J. Schmittbuhl, F. Renard, J. P. Gratier, and R. Toussaint
Phys. Rev. Lett. 93, (2004)
Oct. 18th 2005
IPAM Oct. 2005

8. Misbah C., Renard F., Gratier J.P., Kassner K.,
Geoph. Res. Lett., 31, L6618 (2004).
J. Schmittbuhl, F. Renard, J. P. Gratier, and R. Toussaint
Phys. Rev. Lett. 93, (2004)
Oct. 18th 2005
IPAM Oct. 2005

9. Stylolithes formation
(ex:limestone, queensland,
Australia)
dissolution
Stress-
induced
corrugation
Oct. 18th 2005
IPAM Oct. 2005

10. ATG instability comes to life!
Actin-assisted cell motility
Oct. 18th 2005
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11. J. van der Gucht et al. PNAS, 102, 7847 (2005)
L. A. Cameron et al., PNAS, 96, 4908 (1999).
J. van der Gucht et al. PNAS, 102, 7847 (2005)
Oct. 18th 2005
IPAM Oct. 2005

12. at bead/layer interface
Actin Polymerization
at bead/layer interface
P. Peyla, C. Misbah, preprint (2005)
Oct. 18th 2005
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13. Physical picture of the instability
solid
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14. Physical picture of the instability
solid
Instability unavoidable
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15. Typical lengthscales of the pattern
Strain due to protuberance
Strain energy gain
Surface energy loss
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16. Oct. 18th 2005
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17. For
For
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18. Spencer Meiron (steady-states, 1994)
Yang and Srolovitz (1993)
Kassner and Misbah (1994)
Spencer Meiron (steady-states, 1994)
Oct. 18th 2005
IPAM Oct. 2005

19. Sound speed, finite interface width
Surface
tension
effect
Stress effect
Close to a crack
Sound speed, finite interface width
Oct. 18th 2005
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20. Simple ansatz Cycloid (Chui,Gao, 1993)
Double cycloid (conformal mapping,
Kassner, Misbah, 2001)
, derivation of groove velocities
Multicycloids (Kohlert, Kassner, Misbah, 2003)
(good agreement with numerics with few modes)
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IPAM Oct. 2005

21. Phase-field approach: singularity?
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22. Phase field models Sharp interface Diffuse interface Oct. 18th 2005
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23. Reference state 1 : stress=0 when strain=0
Ref. state 2:
Zero strain is no stress free
Oct. 18th 2005
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24. If ref. state: strain is zero when when stress is
If equilibrium:
If ref. state: strain is zero when when stress is
BC:
For z=0
There is no stress a all!
Because
Oct. 18th 2005
IPAM Oct. 2005

25. If ref. state: strain is zero when when stress is
If equilibrium:
If ref. state: strain is zero when when stress is
BC:
Plays the role of a unixial stress
Oct. 18th 2005
IPAM Oct. 2005

26. Gas (liq., vac.) Diffuse Solid Viewed as the work of external force
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27. gas
solid
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28. Sharp interface limit, asymptotics
Is a Singular perturbation
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29. Outer solution (regular)
Inner solution (singular)
Matching inner-outer solutions
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30. Outer solutions: + Lamé Inner solutions: (1) Zeroth order:
(at all orders)
And BC
(2) First order:
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31. Main Results 1) Increase of the amplitude without bound
2) Phase-field supresses finite time singularity
3) Perpetual coarsening
4) A finite interface width
« Yield stress »
5) Final groove velocity
Oct. 18th 2005
IPAM Oct. 2005

32. Stress accumulation in the grooves, fracture?
1D dynamics
Stress accumulation in the grooves, fracture?
Oct. 18th 2005
IPAM Oct. 2005

33. Coarsening
Mass flux
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34. Exceptions in 1d with no noise!
Coarsening
Mass flux
If non conserved:
Exceptions in 1d with no noise!
Oct. 18th 2005
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35. Volume variation ~ surface
Contact coalescence
Volume variation ~ surface
Oct. 18th 2005
IPAM Oct. 2005

36. Coarsening dominated by elasticity
conserved
nonconserved
In progress
(cycloids show driving force
independent of R)
Agreement with the experiment of Koehn et al.,Geochimica and Cosmochimica Acta, 2004
Oct. 18th 2005
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37. Heteroepitaxy
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38. Partial relaxation Stressed film Oswald ripening?
Narrow size observed InGaAs/GaAs, InAs/inP, InAS/InGaAs, …...
Oct. 18th 2005
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39. =step energy/elastic energy
Monoatomic films
substrate
Elastic
monopoles
coverage
=step energy/elastic energy
Marchenko-Parshin (1980) and Marchenko 1992
Alerhand et al
Oct. 18th 2005
IPAM Oct. 2005

40. (Tersoff, Villain, Müller, Kern….)
Coasening should be inevitable!
Gain in elastic energy and in
surface energy
Oct. 18th 2005
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41. 1) In the pure thermodynamical limit, does coarsening persist?
Open questions
1) In the pure thermodynamical limit, does coarsening
persist?
2) Is it thermodynamical or kinetical? In the first case
which ingredients would supress coarsening?
Coarsening is subtle (Politi, Misbah, Phys. Rev. Lett. 2004)
3) In Dynamical simulations: coarsening stops or
slowed down?
4) Some systems QD form under compression but not
under tension!
5) Cell motility: bead-gel friction decisive?
Oct. 18th 2005
IPAM Oct. 2005