Boundary integral equations for isotropic linear elasticity

Abstract

This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lam\'e coefficients in the form of a bounded domain of arbitrary shape surrounded by a background material. In the simple case of a spherical inclusion, the vector spherical harmonics consist of eigenfunctions of the single and double layer boundary operators and we provide their spectra. Further, in the case of many spherical inclusions with isotropic materials, each with its own set of Lam\'e parameters, we propose an integral equation and a subsequent Galerkin discretization using the vector spherical harmonics and apply the discretization to several numerical test cases.