Duality arguments for linear elasticity problems with incompatible deformation fields

TL;DR

This paper establishes existence, uniqueness, and homogenization results for linear elasticity problems involving incompatible deformation fields and plastic slips in non-homogeneous crystals, advancing understanding of composite material behavior.

Contribution

It introduces duality arguments to prove well-posedness and demonstrates the stability of these problems under G-convergence, linking microscopic plasticity to macroscopic properties.

Findings

Proved existence and uniqueness of solutions for elasticity with plastic slips.

Showed the class of problems is closed under G-convergence.

Derived homogenized models capturing macroscopic behavior of composites with plastic deformation.

Abstract

We prove existence and uniqueness for solutions to equilibrium problems for free-standing, traction-free, non homogeneous crystals in the presence of plastic slips. Moreover we prove that this class of problems is closed under G-convergence of the operators. In particular the homogenization procedure, valid for elliptic systems in linear elasticity, depicts the macroscopic features of a composite material in the presence of plastic deformation.