On the Mechanics of Damage-Susceptible Poroelastic Media

Selvadurai, A. P. S.

doi:10.4028/www.scientific.net/kem.251-252.363

Cited by 5 publications

(4 citation statements)

References 36 publications

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“…The studies in these areas are numerous and no attempt is made here to provide a comprehensive coverage. Important articles related to geotechnical and geoscience applications of THM behavior are provided in Selvadurai and Nguyen [28]; Selvadurai [29][30][31][32][33][34]; Khalili and Selvadurai [35]; Selvadurai and Shirazi [36]; Nguyen et al [37]; Selvadurai and Suvorov [11,38,39]; Najari and Selvadurai [40]; and Selvadurai et al [8]. In fluid-saturated porous media, the externally applied stresses are partitioned between the stresses carried by the porous skeleton and the stresses carried by the pore fluid.…”

Section: Introductionmentioning

confidence: 99%

On the Poroelastic Biot Coefficient for a Granitic Rock

Selvadurai

2021

Geosciences

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The Biot coefficient is a parameter that is encountered in the theory of classical poroelasticity, dealing with the mechanics of a fluid-saturated porous medium with elastic grains and an elastic skeletal structure. In particular, the coefficient plays an important role in the partitioning of externally applied stresses between the pore fluid and the porous skeleton. The conventional approach for estimating the Biot coefficient relies on the mechanical testing of the poroelastic solid, in both a completely dry and a fully saturated state. The former type of tests to determine the skeletal compressibility of the rock can be performed quite conveniently. The latter tests, which determine the compressibility of the solid material constituting the porous skeleton, involve the mechanical testing of the fully saturated rock. These tests are challenging when the rock has a low permeability, since any unsaturated regions of the rock can influence the interpretation of the compressibility of the solid phase composing the porous rock. An alternative approach to the estimation of the solid grain compressibility considers the application of the multi-phasic theories for the elasticity of composite materials, to estimate the solid grain compressibility. This approach requires the accurate determination of the mineralogical composition of the rock using XRD, and the estimation of the elasticity characteristics of the minerals by appealing to published literature. This procedure is used to estimate the Biot coefficient for the Lac du Bonnet granite obtained from the western region of the Canadian Shield.

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Section: Introductionmentioning

confidence: 99%

On the Poroelastic Biot Coefficient for a Granitic Rock

Selvadurai

2021

Geosciences

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“…The importance of the coupling between structural mechanics and fluid dynamics in the damage of deformable porous media has been investigated by several authors [24,22,34]. In the present study, we focus on a particular aspect of this coupling and we aim at characterizing and quantifying the influence of structural viscoelasticity on the biomechanical and fluid-dynamical responses to sudden changes in stress conditions.…”

Section: Introductionmentioning

confidence: 98%

The role of structural viscoelasticity in deformable porous media with incompressible constituents: Applications in biomechanics

Verri

Guidoboni²,

Bociu³

et al. 2018

Mathematical Biosciences &Amp; Engineering

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The main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in external applied loads. Models of deformable porous media with incompressible constituents are often utilized to describe the behavior of biological tissues, such as cartilages, bones and engineered tissue scaffolds, where viscoelastic properties may change with age, disease or by design. Here, for the first time, we show that the fluid velocity within the medium could increase tremendously, even up to infinity, should the external applied load experience sudden changes in time and the structural viscoelasticity be too small. In particular, we consider a one-dimensional poro-visco-elastic model for which we derive explicit solutions in the cases where the external applied load is characterized by a step pulse or a trapezoidal pulse in time. By means of dimensional analysis, we identify some dimensionless parameters that can aid the design of structural properties and/or experimental conditions as to ensure that the fluid velocity within the medium remains bounded below a certain given threshold, thereby preventing potential tissue damage. The application to confined compression tests for biological tissues is discussed in detail. Interestingly, the loss of viscoelastic tissue properties has been associated with various disease conditions, such as atherosclerosis, Alzheimer's disease and glaucoma. Thus, the findings of this work may be relevant to many applications in biology and medicine.

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“…The pioneering works of Terzaghi 1 and Biot 2,3 considered soil consolidation problems. Other applications can be found in geomechanics, petroleum engineering, hydrogeology 4–6 or even in biological modeling 7–9 . For the description of thermodynamical aspects of poroelastic models, we refer to References 4,5,10,11.…”

Section: Introductionmentioning

confidence: 99%

Robust block diagonal preconditioners for poroelastic problems with strongly heterogeneous material

Luber,

Sysala

2023

Numerical Linear Algebra App

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This paper focuses on the analysis and the solution of the saddle‐point problem arising from a three‐field formulation of Biot's model of poroelasticity, discretized in time by the implicit Euler method. A block diagonal‐preconditioner, based on the Schur complement, is analyzed on a functional level and compared with two other block‐diagonal preconditioners having a similar structure. The problem is discretized in space using mixed finite elements and solved with appropriate iterative solvers, incorporating the investigated preconditioners. The solvers are tested on numerical examples inspired by geotechnical practice, with particular attention devoted to the solvers' robustness concerning strong heterogeneity in permeability.

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On the Mechanics of Damage-Susceptible Poroelastic Media

Cited by 5 publications

References 36 publications

On the Poroelastic Biot Coefficient for a Granitic Rock

On the Poroelastic Biot Coefficient for a Granitic Rock

The role of structural viscoelasticity in deformable porous media with incompressible constituents: Applications in biomechanics

Robust block diagonal preconditioners for poroelastic problems with strongly heterogeneous material

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