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Volume 40, Issue 6
Boundary Integral Equations for Isotropic Linear Elasticity

Benjamin Stamm & Shuyang Xiang

DOI: 10.4208/jcm.2103-m2019-0031

J. Comp. Math., 40 (2022), pp. 835-864.

Published online: 2022-08

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  • 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.

  • Keywords

Isotropic elasticity, Boundary integral equation, Spherical inclusions, Vector spherical harmonics, Layer potentials.

  • AMS Subject Headings

65R20, 65N38, 74B05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

best@acom.rwth-aachen.de (Benjamin Stamm)

vanillaxiangshuyang@gmail.com (Shuyang Xiang)

  • BibTex
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  • TXT
@Article{JCM-40-835, author = {Stamm , Benjamin and Xiang , Shuyang}, title = {Boundary Integral Equations for Isotropic Linear Elasticity}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {40}, number = {6}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2103-m2019-0031}, url = {http://global-sci.org/intro/article_detail/jcm/20838.html} }
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 -

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.

Stamm , Benjamin and Xiang , Shuyang. (2022). Boundary Integral Equations for Isotropic Linear Elasticity. Journal of Computational Mathematics. 40 (6). 835-864. doi:10.4208/jcm.2103-m2019-0031
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