Gradient Theory for Plasticity via Homogenization of Discrete Dislocations
نویسندگان
چکیده
In this paper, we deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations. We restrict our analysis to the case of a cylindrical symmetry for the crystal in exam, so that the mathematical formulation will involve a two dimensional variational problem. The dislocations are introduced as point topological defects of the strain fields, for which we compute the elastic energy stored outside the so called core region. We show that the Γ-limit as the core radius ε tends to zero and the number of dislocations tends to infinity of this energy (suitably rescaled), takes the form
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