Calculus of Variations and Geometric Measure Theory
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Variational analysis of material defects and crystal plasticity

Adriana Garroni (Dip. Mat. Univ. Roma ``La Sapienza'')

created by gelli on 31 Jan 2016

10 feb 2016 -- 15:30

Aula Magna (Dipartimento di Matematica di Pisa)

Abstract.

Dislocations are line defects in the crystalline structure of metals. They are considered the main mechanism for plastic deformation and their interaction at the microscopic scale are relevant to understand complex phenomena as yielding and hardening. I will present the derivation, in terms of Gamma-convergence, of three-dimensional variational models for material defects and crystal plasticity. Depending on the energy scaling one can obtain a line tension energy associated to dislocations in 3D or a gradient theory for plasticity. The rigorous analysis shows that in some cases the effective models may reveal the presence of relaxation and formation of microstructure.

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