13 January, 2010

Lecture 1: Inhomogeneous elastic response of amorphous solids

Outline

- Elastic constants for a system interacting with pair forces : fluctuation formulae, direct measurement; local definitions of elastic constants

- Non affine displacement field, convergence to the macroscopic limit (vibrations, correlation functions of nonaffine displacements), response to a localized force

- Boson peak and elastic heterogeneities

- Scaling of elastic constants at J point

 

Lecture 2: Large deformations, rheology, plasticity

Outline

- low temperature, quasi static deformation in Lennard-Jones and other systems

- review of existing theories: mean field models, correlated elasto plastic models

- some results from MD: prediction of plastic activity, avalanche size, low strain rate limit

- high T rheology, effective temperature ideas

 

References and suggested reading

  1. Microscopic elasticity of complex systems, J-L. Barrat Lecture Notes for the Erice Summer School 2005 Computer Simulations in Condensed Matter: from Materials to Chemical Biology http://arxiv.org/abs/cond-mat/0601653
  2. F. Leonforte, A. Tanguy, J.P. Wittmer, J.-L. Barrat Physical Review B 70 (2004) 014203 http://arxiv.org/abs/cond-mat/0309623
  3. On the Rigidity of Amorphous Solids, Matthieu Wyart Annales de Physique, Vol. 30 No. 3 (May- June 2005) http://arxiv.org/abs/cond-mat/0512155
  4. Nonaffine Correlations in Random Elastic Media B.A. DiDonna, T. C. Lubensky Phys Rev E 72, 066619 (2005) http://arxiv.org/abs/cond-mat/0506456
  5. Plastic Response of a 2D Lennard-Jones amorphous solid: Detailed analysis of the local rearrangements at very slow strain-rate Anne Tanguy, Fabien Leonforte, J.-L. Barrat Euto Phys. Jl. E, 20, 3, 355 (2006) http://arxiv.org/abs/cond-mat/0605397
  6. Slow flows of yield stress fluids: complex spatio-temporal behaviour within a simple elasto-plastic model Guillemette Picard, Armand Ajdari, Francois Lequeux, Lyderic Bocquet Phys. Rev. E, 71, 010501(R) http://arxiv.org/abs/cond-mat/0409452
  7. Nonequilibrium dynamics and fluctuation-dissipation relation in a sheared fluid, LudovicBerthier, Jean-Louis Barrat J. Chem. Phys. 116, 6228 (2002) http://arxiv.org/abs/condmat/0111312