Meso-scale models and approximate solutions for solids containing clouds of voids

TL;DR

This paper develops meso-scale models and explicit asymptotic solutions for linear elasticity problems in highly perforated solids with non-periodic voids, providing uniform approximations beyond homogenization methods.

Contribution

It introduces a novel meso-scale approximation approach for non-periodic perforated domains in elasticity, with explicit formulas and remainder estimates.

Findings

Uniform asymptotic formulas derived

Applicable to non-periodic perforated domains

Provides explicit error estimates

Abstract

For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of meso-scale approximations. There are no assumptions of periodicity involved in the description of the geometry of the domain. The size of the perforations is small compared to the minimal separation between neighbouring defects and here we discuss a class of problems in perforated domains, which are not covered by the homogenisation approximations. The meso-scale approximations presented here are uniform. Explicit asymptotic formulae are supplied with the remainder estimates.