Homogenization for A-quasiconvexity with variable coefficients

TL;DR

This paper extends homogenization theory for oscillating energies under variable coefficient differential constraints, utilizing A-quasiconvexity and two-scale convergence to generalize previous constant-coefficient results.

Contribution

It introduces a homogenization framework for A-quasiconvex energies with variable coefficients, broadening the scope of prior constant-coefficient models.

Findings

Generalized homogenization results for variable coefficient constraints

Identified relaxed energy via A-quasiconvexity with variable coefficients

Extended previous constant-coefficient homogenization theories

Abstract

A homogenization result for a family of oscillating integral energies is presented, where the fields under consideration are subjected to first order linear differential constraints depending on the space variable x. The work is based on the theory of A-quasiconvexity with variable coefficients and on two-scale convergence techniques, and generalizes the previously obtained results in the case in which the differential constraints are imposed by means of a linear first order differential operator with constant coefficients. The identification of the relaxed energy in the framework of A-quasiconvexity with variable coefficients is also recovered as a corollary of the homogenization result.