Strain-Gradient Plasticity as the Γ-Limit of a Nonlinear Dislocation Energy with Mixed Growth

2018/06/13 by Ginster, Janusz · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.05067

Abstract

In this paper a we derive by means of Γ-convergence a macroscopic strain-gradient plasticity from a semi-discrete model for dislocations in an infinite cylindrical crystal. In contrast to existing work, we consider an energy with subquadratic growth close to the dislocations. This allows to treat the stored elastic energy without the need to introduce an ad-hoc cut-off radius. As the main tool to prove a complementing compactness statement, we present a generalized version of the geometric rigidity result for fields with non-vanishing curl. A main ingredient is a fine decomposition result for L¹-functions whose divergence is in certain critical Sobolev spaces.

Cited by

• On the formation of microstructure and the occurrence of vortices in a singularly perturbed energy related to helimagnetism: a scaling law result

Related

• Gradient theory for plasticity via homogenization of discrete dislocations
• From Volterra dislocations to strain-gradient plasticity
• Derivation of strain-gradient plasticity from a generalized Peierls-Nabarro model
• A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations
• Strain gradient visco-plasticity with dislocation densities contributing to the energy