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The method of fundamental solution for 3‐D wave scattering in a fluid‐saturated poroelastic infinite domain
Author(s) -
Liu Zhongxian,
Wang Zhikun,
Cheng Alexander H.D.,
Liang Jianwen,
Wang Chuchu
Publication year - 2018
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2836
Subject(s) - poromechanics , scattering , boundary value problem , boundary element method , mathematical analysis , shear modulus , mathematics , geometry , mechanics , physics , finite element method , materials science , porosity , porous medium , optics , composite material , thermodynamics
Summary By using a complete set of poroelastodynamic spherical wave potentials (SWPs) representing a fast compressional wave P I , a slow compressional wave P II , and a shear wave S with 3 vectorial potentials (not all are independent), a solution scheme based on the method of fundamental solution (MFS) is devised to solve 3‐D wave scattering and dynamic stress concentration problems due to inhomogeneous inclusions and cavities embedded in an infinite poroelastic domain. The method is verified by comparing the result with the elastic analytical solution, which is a degenerated case, as well as with poroelastic solution obtained using other numerical methods. The accuracy and stability of the SWP‐MFS are also demonstrated. The displacement, hoop stress, and fluid pore pressure around spherical cavity and poroelastic inclusion with permeable and impermeable boundary are investigated for incident plane P I and SV waves. The scattering characteristics are examined for a range of material properties, such as porosity and shear modulus contrast, over a range of frequency. Compared with other boundary‐based numerical strategy, such as the boundary element method and the indirect boundary integral equation method, the current SWP‐MFS is a meshless method that does not need elements to approximate the geometry and is free from the treatment of singularities. The SWP‐MFS is a highly accurate and efficient solution methodology for wave scattering problems of arbitrary geometry, particularly when a part of the domain extends to infinity.