TY - JOUR
T1 - Boundary Integral Equations for Isotropic Linear Elasticity
AU - Stamm , Benjamin
AU - Xiang , Shuyang
JO - Journal of Computational Mathematics
VL - 6
SP - 835
EP - 864
PY - 2022
DA - 2022/08
SN - 40
DO - http://doi.org/10.4208/jcm.2103-m2019-0031
UR - https://global-sci.org/intro/article_detail/jcm/20838.html
KW - Isotropic elasticity, Boundary integral equation, Spherical inclusions, Vector spherical harmonics, Layer potentials.
AB - <p style="text-align: justify;">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.</p>