Homogenization of singular integrals in W^{1,\infty}

TL;DR

This paper establishes a periodic homogenization result for nonconvex integral functionals with singular boundary behavior, applicable to hyperelasticity with bounded deformation gradients.

Contribution

It introduces a homogenization framework for nonconvex integrals with singularities near boundary constraints, advancing the mathematical understanding of hyperelastic materials.

Findings

Proved homogenization for nonconvex integrals with boundary singularities.

Applied the theory to hyperelasticity with bounded gradients.

Extended homogenization techniques to singular integral functionals.

Abstract

A periodic homogenization result of nonconvex integral functionals in the vectorial case with convex bounded constraints on gradients is proved. The class of integrands considered have singular behavior near the boundary of the convex set of the constraints. We apply the result to the case of periodic homogenization in hyperelasticity for bounded gradients of deformations.