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Stress induced instabilities in material science and biology

Stress induced instabilities in material science and biology. C. Misbah, CNRS and Univ. J. Fourier Grenoble I. Los Angeles October. 2005. Uniaxial stress. Biaxial stress. Questions. Melt, vapor. 1) Front growth or recession?. Solid. 2) Planar front stable?. Solid. 3) Ultimate stage?.

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Stress induced instabilities in material science and biology

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

  2. Uniaxial stress Biaxial stress IPAM Oct. 2005

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

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

  6. Swelling or shrinkage of gels Clamped at bottom Gel swelling T. Tanaka, H. Tanaka, Kawasaki, Sekimoto, Onuki 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, 238501 (2004) 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, 238501 (2004) IPAM Oct. 2005

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

  10. ATG instability comes to life! Actin-assisted cell motility IPAM Oct. 2005

  11. L. A. Cameron et al., PNAS, 96, 4908 (1999). J. van der Gucht et al. PNAS, 102, 7847 (2005) IPAM Oct. 2005

  12. Actin Polymerization at bead/layer interface P. Peyla, C. Misbah, preprint (2005) IPAM Oct. 2005

  13. Physical picture of the instability solid IPAM Oct. 2005

  14. Physical picture of the instability solid Instability unavoidable IPAM Oct. 2005

  15. Typical lengthscales of the pattern Strain due to protuberance Strain energy gain Surface energy loss IPAM Oct. 2005

  16. IPAM Oct. 2005

  17. For For IPAM Oct. 2005

  18. Yang and Srolovitz (1993) Kassner and Misbah (1994) Spencer Meiron (steady-states, 1994) IPAM Oct. 2005

  19. Surface tension effect Stress effect Close to a crack Sound speed, finite interface width IPAM Oct. 2005

  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) IPAM Oct. 2005

  21. Phase-field approach: singularity? IPAM Oct. 2005

  22. Phase field models Sharp interface Diffuse interface IPAM Oct. 2005

  23. Reference state Reference state 1 : stress=0 when strain=0 Ref. state 2: Zero strain is no stress free IPAM Oct. 2005

  24. If equilibrium: If ref. state: strain is zero when when stress is BC: For z=0 There is no stress a all! Because IPAM Oct. 2005

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

  26. Viewed as the work of external force Gas (liq., vac.) Diffuse Solid IPAM Oct. 2005

  27. gas solid IPAM Oct. 2005

  28. Sharp interface limit, asymptotics Is a Singular perturbation IPAM Oct. 2005

  29. Outer solution (regular) Inner solution (singular) Matching inner-outer solutions IPAM Oct. 2005

  30. + Lamé Outer solutions: Inner solutions: (1) Zeroth order: (at all orders) And BC (2) First order: IPAM Oct. 2005

  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 IPAM Oct. 2005

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

  33. Coarsening Mass flux IPAM Oct. 2005

  34. Coarsening Mass flux If non conserved: Exceptions in 1d with no noise! IPAM Oct. 2005

  35. Contact coalescence Volume variation ~ surface IPAM Oct. 2005

  36. Coarsening dominated by elasticity conserved nonconserved (cycloids show driving force independent of R) In progress Agreement with the experiment of Koehn et al.,Geochimica and Cosmochimica Acta, 2004 IPAM Oct. 2005

  37. Heteroepitaxy IPAM Oct. 2005

  38. Partial relaxation Stressed film Oswald ripening? Narrow size observed InGaAs/GaAs, InAs/inP, InAS/InGaAs, …... IPAM Oct. 2005

  39. Monoatomic films substrate Elastic monopoles =step energy/elastic energy coverage Marchenko-Parshin (1980) and Marchenko 1992 Alerhand et al. 1989. IPAM Oct. 2005

  40. (Tersoff, Villain, Müller, Kern….) Coasening should be inevitable! Gain in elastic energy and in surface energy IPAM Oct. 2005

  41. 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? IPAM Oct. 2005

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