Year: 2022
Author: Benjamin Stamm, Shuyang Xiang
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 6 : 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2103-m2019-0031
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 6 : pp. 835–864
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Isotropic elasticity Boundary integral equation Spherical inclusions Vector spherical harmonics Layer potentials.