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Review Articles

Poroelastodynamics: Linear Models, Analytical Solutions, and Numerical Methods

[+] Author and Article Information
Martin Schanz

Institute of Applied Mechanics, Graz University of Technology, Technikerstr. 4, 8010 Graz, Austriam.schanz@tugraz.at

Appl. Mech. Rev 62(3), 030803 (Mar 31, 2009) (15 pages) doi:10.1115/1.3090831 History: Received September 25, 2008; Revised September 28, 2008; Published March 31, 2009

This article presents an overview on poroelastodynamic models and some analytical solutions. A brief summary of Biot’s theory and of other poroelastic dynamic governing equations is given. There is a focus on dynamic formulations, and the quasistatic case is not considered at all. Some analytical solutions for special problems, fundamental solutions, and Green’s functions are discussed. The numerical realization with two different methodologies, namely, the finite element method and the boundary element method, is reviewed.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Geometry and boundary conditions of the poroelastic column

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Figure 2

Comparison of Biot’s theory (denoted as “Biot”), the simplified theory (denoted as “simple poro”), and the theory using a static Darcy’s law (denoted as “static Darcy”): displacement response of a poroelastic column due to a Heaviside stress load

Grahic Jump Location
Figure 3

Comparison of Biot’s theory (denoted as “Biot”), the simplified theory (denoted as “simple poro”), and the theory using a static Darcy’s law (denoted as “static Darcy”): pressure response of a poroelastic column at the bottom for different permeabilities κ

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Figure 4

Comparison of TPM and Biot: response of a poroelastic column due to a Heaviside stress load

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