Boundary Integral Equations for Isotropic Linear Elasticity

Journal of Computational Mathematics, vol. 40, pp. 835–864

Abstract

This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lamé 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 Lamé 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.

Authors 2

1. Benjamin Stamm Aachen Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   Department of Mathematics, RWTH Aachen University, Aachen, Germany

2. Shuyang Xiang corresponding Aachen Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   Department of Mathematics, RWTH Aachen University, Aachen, Germany