Dynamic characterization of poroelastic materials

Kim, Y. K.; Kingsbury, Herbert B.

doi:10.1007/bf02328654

Cited by 46 publications

(15 citation statements)

References 16 publications

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“…This deformation also preserves the pore geometry, hence there is no porosity change, = 0. As observed from (24), the solid volumetric deformation is characterized by…”

Section: Intrinsic Materials Constants and Fundamental Deformation Modesmentioning

confidence: 88%

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Intrinsic poroelasticity constants and a semilinear model

Cheng

Abousleiman

2007

Num Anal Meth Geomechanics

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SUMMARYThis paper presents an intrinsic micromechanical model for poroelasticity that leads to an alternative set of material constants. In the intrinsic model, the deformations of the solid phase, the fluid phase, and the pore space are explicitly modeled, and porosity is considered as a primary variable. The averaging process distinguishes an external frame surface averaging and an internal phase volume averaging. The variational principle leads to a porosity equilibrium equation that defines the nonlinear deformation of pore volume. Three fundamental deformation modes with their intrinsic material constants are identified: the shape preserving volumetric deformation of the solid phase, the porosity change due to solid grain rearrangement, and the porosity change associated with the microanisotropy and microinhomogeneity of solid phase. The linearized model is fully consistent with the Biot theory of poroelasticity. A semilinear model considering only porosity deformation nonlinearity with linear material constant leads to a universal exponential strain hardening law. The theory is tested against laboratory data of sandstone.

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“…This deformation also preserves the pore geometry, hence there is no porosity change, = 0. As observed from (24), the solid volumetric deformation is characterized by…”

Section: Intrinsic Materials Constants and Fundamental Deformation Modesmentioning

confidence: 88%

“…Equation (24) indicates that the solid mean compressive stress is dependent not only on the solid volumetric strain, but also on the porosity change. For the fluid phase, a similar construction leads to the simple constitutive relation…”

Section: Micromechanical Constitutive Relationsmentioning

confidence: 99%

Intrinsic poroelasticity constants and a semilinear model

Cheng

Abousleiman

2007

Num Anal Meth Geomechanics

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“…In the following tests, the used material data are those of a rock [31] (Berea sandstone) in case of the column and for the half space example those of a coarse water saturated soil [32]. The data for both materials are collected in Table I.…”

Section: Numerical Examplesmentioning

confidence: 99%

Wave propagation in a simplified modelled poroelastic continuum: fundamental solutions and a time domain boundary element formulation

Schanz

Struckmeier

2005

Numerical Meth Engineering

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SUMMARYIn finite element formulations for poroelastic continua a representation of Biot's theory using the unknowns solid displacement and pore pressure is preferred. Such a formulation is possible either for quasi-static problems or for dynamic problems if the inertia effects of the fluid are neglected. Contrary to these formulations a boundary element method (BEM) for the general case of Biot's theory in time domain has been published (Wave Propagation in Viscoelastic and Poroelastic Continua: A Boundary Element Approach. Lecture Notes in Applied Mechanics. Springer: Berlin, Heidelberg, New York, 2001.). If the advantages of both methods are required it is common practice to couple both methods. However, for such a coupled FE/BE procedure a BEM for the simplified dynamic Biot theory as used in FEM must be developed.Therefore, here, the fundamental solutions as well as a BE time stepping procedure is presented for the simplified dynamic theory where the inertia effects of the fluid are neglected. Further, a semi-analytical one-dimensional solution is presented to check the proposed BE formulation. Finally, wave propagation problems are studied using either the complete Biot theory as well as the simplified theory. These examples show that no significant differences occur for the selected material.

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“…[16] In this paper we focus on the examination of the different BEM operators which are needed to solve a mixed boundary value problem (BVP) through the so-called direct approach. For simplicity we restrict ourselves to the Dirichlet problem, i.e.…”

Section: Boundary Element Formulation In Laplace Domainmentioning

confidence: 99%

“…For the measured material data of Berea sandstone [16], c.f. Table 1, the entries of the system matrix V ij (K ij ) differ by magnitudes.…”

Section: Boundary Element Formulation In Laplace Domainmentioning

confidence: 99%

A Chebyshev Interpoaltion-Based Fast Multipole Method for Poroelasticity

Knöbl¹,

Traub²,

Schanz³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The treatment of porous media with the BEM exhibits some problems, which are common also for the Finite Element Method, but also some BEM specific ones. The three main problems are: First, the multiphase system requires four degrees of freedom per node, leading to large matrices even for small problems. Since the BEM matrices are densely populated, this makes the method prohibitive for large problem sizes. Second, due to the different physical nature of the degrees of freedom the matrix entries vary over several orders of magnitude. Third, the fundamental solution of poroelasticity is computationally expensive.We present a FM-BEM that circumvents those points: The Chebyshev interpolation-based FMM significantly reduces the memory consumption of the system matrix and thus allows for larger problem sizes to be treated. As well, it requires fewer evaluations of the fundamental solution. To employ an iterative solver, the use of a transformation of the material data is mandatory.

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Dynamic characterization of poroelastic materials

Cited by 46 publications

References 16 publications

Intrinsic poroelasticity constants and a semilinear model

Intrinsic poroelasticity constants and a semilinear model

Wave propagation in a simplified modelled poroelastic continuum: fundamental solutions and a time domain boundary element formulation

A Chebyshev Interpoaltion-Based Fast Multipole Method for Poroelasticity

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