Asymptotic Analysis of a Coupled System of Nonlocal Equations with Oscillatory Coefficients
Analysis of PDEs
2021-06-22 v2
Abstract
In this paper we study the asymptotic behavior of solutions to systems of strongly coupled integral equations with oscillatory coefficients. The system of equations is motivated by a peridynamic model of the deformation of heterogeneous media that additionally accounts for short-range forces. We consider the vanishing nonlocality limit on the same length scale as the heterogeneity and show that the system's effective behavior is characterized by a coupled system of local equations that are elliptic in the sense of Legendre-Hadamard. This effective system is characterized by a fourth-order tensor that shares properties with Cauchy elasticity tensors that appear in the classical equilibrium equations for linearized elasticity.
Keywords
Cite
@article{arxiv.1909.08020,
title = {Asymptotic Analysis of a Coupled System of Nonlocal Equations with Oscillatory Coefficients},
author = {Tadele Mengesha and James M. Scott},
journal= {arXiv preprint arXiv:1909.08020},
year = {2021}
}