Modeling of Crystal Plasticity by Using a Non-Convex Energy Based on GL(2, Z) Invariance

Orateur : Umut SALMAN (LSPM UPR 3407 CNRS, Université Paris 13)

For micro- and nano-sized samples, dislocation-mediated crystal plasticity is radically different from that described by classical engineering theories. At the microscale, plasticity evolves in a disordered manner through a sequence of intermittent events involving collective motion of dislocations and their interaction with each other and with existing lattice defects. Detailed mathematical modeling of these processes remains a major challenge in materials science. We present a mesoscopic post-DDD approach which involves constructing a non-convex energy invariant under the full symmetry group of lattices - such as GL(2, Z) in the 2-d case. The model is thus informed by the inherent structure of the material, and is largely free of arbitrariness when dealing with the fast topological changes in dislocation configurations such as nucleation, annihilation, interaction with obstacles and with various other entanglements.

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