### BOUNDARY INTEGRAL EQUATIONS FOR ISOTROPIC LINEAR ELASTICITY

Benjamin Stamm, Shuyang Xiang

1. Department of Mathematics, RWTH Aachen University, Aachen, Germany
• Received:2019-02-08 Revised:2020-01-19 Online:2022-11-15 Published:2022-11-18
• Contact: Benjamin Stamm, Email: best@acom.rwth-aachen.de
• Supported by:
BS acknowledges the funding from the German Academic Exchange Service (DAAD) from funds of the Bundesministeriums für Bildung und Forschung (BMBF) for the project Aa-Par-T (Project-ID 57317909). SX acknowledges the funding from the PICSCNRS as well as the PHC PROCOPE 2017 (Project N37855ZK).

Benjamin Stamm, Shuyang Xiang. BOUNDARY INTEGRAL EQUATIONS FOR ISOTROPIC LINEAR ELASTICITY[J]. Journal of Computational Mathematics, 2022, 40(6): 835-864.

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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