Asymptotic Expansions for High-Contrast Linear Elasticity

TL;DR

This paper develops asymptotic expansions to analyze high-contrast linear elasticity problems, providing a mathematical framework for understanding how material heterogeneity affects elastic behavior.

Contribution

It introduces a novel asymptotic expansion method for high-contrast elasticity problems and analyzes its convergence in the $H^1$ norm.

Findings

Derived an asymptotic expansion for high-contrast elasticity

Proved convergence of the expansion in the $H^1$ norm

Provides a new analytical tool for heterogeneous elasticity analysis

Abstract

We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the $H^1$ norm.