Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization.


Journal Article

A compact Green's function for general dispersive anisotropic poroelastic media in a full-frequency regime is presented for the first time. First, starting in a frequency domain, the anisotropic dispersion is exactly incorporated into the constitutive relationship, thus avoiding fractional derivatives in a time domain. Then, based on the Radon transform, the original three-dimensional differential equation is effectively reduced to a one-dimensional system in space. Furthermore, inspired by the strategy adopted in the characteristic analysis of hyperbolic equations, the eigenvector diagonalization method is applied to decouple the one-dimensional vector problem into several independent scalar equations. Consequently, the fundamental solutions are easily obtained. A further derivation shows that Green's function can be decomposed into circumferential and spherical integrals, corresponding to static and transient responses, respectively. The procedures shown in this study are also compatible with other pertinent multi-physics coupling problems, such as piezoelectric, magneto-electro-elastic and thermo-elastic materials. Finally, the verifications and validations with existing analytical solutions and numerical solvers corroborate the correctness of the proposed Green's function.

Full Text

Duke Authors

Cited Authors

  • Zhan, Q; Zhuang, M; Fang, Y; Liu, J-G; Liu, QH

Published Date

  • January 30, 2019

Published In

Volume / Issue

  • 475 / 2221

Start / End Page

  • 20180610 -

PubMed ID

  • 30760962

Pubmed Central ID

  • 30760962

Electronic International Standard Serial Number (EISSN)

  • 1471-2946

International Standard Serial Number (ISSN)

  • 1364-5021

Digital Object Identifier (DOI)

  • 10.1098/rspa.2018.0610


  • eng