Journal ArticleDOI
Time domain fundamental solution to Biot's complete equations of dynamic poroelasticity. Part I: Two-dimensional solution†
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In this paper, a transient fundamental solution for Biot's full dynamic two-dimensional equations of poroelasticity is presented, both for the limiting case (early time approximation) and for the general case (general case).About:
This article is published in International Journal of Solids and Structures.The article was published on 1994-05-01. It has received 94 citations till now. The article focuses on the topics: Laplace transform applied to differential equations & Inverse Laplace transform.read more
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Poroelastodynamics: Linear Models, Analytical Solutions, and Numerical Methods
TL;DR: In this paper, an overview on poroelastodynamic models and some analytical solutions is presented, with a focus on dynamic formulations and the quasi-static case is not considered at all.
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Application of 3D time domain boundary element formulation to wave propagation in poroelastic solids
TL;DR: In this paper, a convolution quadrature method was proposed to model the dynamic behavior of a poroelastic material in the time domain, and a time-stepping procedure was obtained based only on the Laplace domain fundamental solution and a linear multistep method.
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Dynamic fundamental solutions for compressible and incompressible modeled poroelastic continua
Martin Schanz,Dobromil Pryl +1 more
TL;DR: In this article, Biot's theory is used to derive fundamental solutions for the u i s − u i f formulation of incompressibility in a two-phase material, where not only each component, the solid and the fluid, may be compressible on the microscopic level but also the skeleton itself possesses a structural compressibility.
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On the Fundamental Solution of Dynamic Poroelastic Boundary Integral Equations in the Time Domain
Behrooz Gatmiri,Mohssen Kamalian +1 more
TL;DR: In this paper, boundary integral equations and Laplace transform domain fundamental solutions to the u-p formulation of two-dimensional dynamic poroelasticity are derived based on the Cleary reciprocal theorem.
Journal ArticleDOI
Dynamic Green’s functions for a poroelastic half-space
Pei Zheng,She-Xu Zhao,Ding Ding +2 more
TL;DR: In this paper, the dynamic responses of a poroelastic half-space to an internal point load and fluid source are investigated in the frequency domain by virtue of a method of displacement potentials.
References
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Handbook of Mathematical Functions
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General Theory of Three‐Dimensional Consolidation
TL;DR: In this article, the number of physical constants necessary to determine the properties of the soil is derived along with the general equations for the prediction of settlements and stresses in three-dimensional problems.
Book
A treatise on the mathematical theory of elasticity
TL;DR: Webb's work on elasticity as mentioned in this paper is the outcome of a suggestion made to me some years ago by Mr R. R. Webb that I should assist him in the preparation of a work on Elasticity.
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Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range
TL;DR: In this article, a theory for the propagation of stress waves in a porous elastic solid containing compressible viscous fluid is developed for the lower frequency range where the assumption of Poiseuille flow is valid.
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Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range
TL;DR: In this paper, the theory of propagation of stress waves in a porous elastic solid developed in Part I for the low-frequency range is extended to higher frequencies, and the breakdown of Poiseuille flow beyond the critical frequency is discussed for pores of flat and circular shapes.