Homogenization of Integral Energies Under Periodically Oscillating Differential Constraints

TL;DR

This paper develops a homogenization framework for integral energies constrained by periodic oscillating differential conditions, utilizing A-quasiconvexity and two-scale convergence methods.

Contribution

It introduces a novel homogenization approach for energies under periodic differential constraints using advanced quasiconvexity and convergence techniques.

Findings

Established homogenization results for oscillating differential constraints.

Extended A-quasiconvexity theory to variable coefficient settings.

Applied two-scale convergence to analyze energy limits.

Abstract

A homogenization result for a family of integral energies is presented, where the fields are subjected to periodic first order oscillating differential constraints in divergence form. The work is based on the theory of A -quasiconvexity with variable coefficients and on two- scale convergence techniques.