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D. Vandembroucq - PMMH, ESPCI

The propagation of a fracture front in a heterogeneous material can be modelled as the advance of an elastic line in a random environment. The competition between elasticity - which tends to smooothen the line-  and disorder - which tends to roughen it - induces a rich phenomenology : scale invariant roughness, avalanche behavior, etc. We will show that beyond scaling invariance, this description of crack propagation as a dynamic phase transition gives us important information on the effective mechanical properties at macroscopic scale. We will also discuss the modelling of plasticity in amorphous materials. In the absence of crystalline lattice, plastic deformation does not result of dislocation motion but of series of very localized reorganizations. Such reorganizations of the structure induce in turn elastic stresses. We will propose a very simple depinning-like model to describe this phenomenon, again characterized by a strong competition between elasticity and disorder.