Abstract
The paper develops theoretical estimates for the parameters that describe the classical theory of poroelasticity for a fluid-saturated porous medium, with a porous elastic skeleton that can ...exhibit imperfect grain contacts. The results for the poroelastic properties predicted from the modelling are compared with experimental results available in the literature.
Fluid-saturated materials are encountered in several areas of engineering and biological applications. Geologic media saturated with water, oil and gas and biological materials such as bone saturated ...with synovial fluid, soft tissues containing blood and plasma and synthetic materials impregnated with energy absorbing fluids are some examples. In many instances such materials can be examined quite successfully by appeal to classical theories of poroelasticity where the skeletal deformations can be modelled as linear elastic. In the case of soft biological tissues and even highly compressible organic geological materials, the porous skeleton can experience large strains and, unlike rubberlike materials, the fluid plays an important role in maintaining the large strain capability of the material. In some instances, the removal of the fluid can render the geological or biological material void of any hyperelastic effects. While the fluid component can be present at various scales and forms, a useful first approximation would be to treat the material as hyperelastic where the fabric can experience large strains consistent with a hyperelastic material and an independent scalar pressure describes the pore fluid response. The flow of fluid within the porous skeleton is defined by Darcy's law for an isotropic material, which is formulated in terms of the relative velocity between the pore fluid and the porous skeleton. It is assumed that the form of Darcy's law remains unchanged during the large strain behaviour. This approach basically extends Biot's theory of classical poroelasticity to include finite deformations. The developments are used to examine the poro-hyperelastic behaviour of certain one-dimensional problems.
Abstract
Fluid-saturated rocks are multi-phasic materials and the mechanics of partitioning the externally applied stresses between the porous skeleton of the rock and the interstitial fluids has to ...take into consideration the mechanical behaviour of the phases. In these studies the porosity of the multi-phasic material is important for estimating the multi-phasic properties and most studies treat the porosity as a scalar measure without addressing the influence of pore shape and pore geometry. This paper shows that both the overall bulk modulus of a porous medium and the Biot coefficient depend on the shape of the pores. Pores with shapes resembling either thin oblate spheroids or spheres are considered. The Mori–Tanaka and the self-consistent methods are used to estimate the overall properties and the results are compared with experimental data. The pore density and the aspect ratio of the spheroidal pores influence the porosity of the geomaterials. For partially saturated rocks, the equivalent bulk modulus of the fluid–gas mixture occupying the pore space can also be obtained. The paper also examines the influence of the pore shape in estimating the Biot coefficient that controls the stress partitioning in fluid-saturated poroelastic materials.
On the inflation of poro-hyperelastic annuli Selvadurai, A.P.S.; Suvorov, A.P.
Journal of the mechanics and physics of solids,
October 2017, 2017-10-00, 20171001, Letnik:
107
Journal Article
Recenzirano
The paper presents the radially and spherically symmetric problems associated with the inflation of poro-hyperelastic regions. The theory of poro-hyperelasticity is a convenient framework for ...modelling the mechanical behaviour of highly deformable materials in which the pore space is saturated with fluids. Including the coupled mechanical responses of both the hyperelastic porous skeleton and the fluid is regarded as an important consideration for the application of the results, particularly to soft tissues encountered in biomechanical applications. The analytical solutions for radially and spherically symmetric problems involving annular domains are used to benchmark the accuracy of a standard computational approach. The paper also generates results applicable to the hyperelastic solutions when coupling is eliminated through the presence of a highly permeable pore structure.
This paper investigates the influence of the development of elasto-plastic failure on the evolution of the Biot coefficient for a fluid-saturated geomaterial. Attention is restricted to the study of ...an elasto-plastic porous skeleton that has a solid phase with failure characteristics corresponding to an isotropic medium with a von-Mises-type failure criterion and an associated flow rule. The evolution of the Biot coefficient with the development of failure is illustrated through specific examples. The assumptions implicit in standard computational approaches for examining poroelastic behavior in the light of these developments are also discussed.
Interfaces possess complex mechanical responses that are governed by several factors including the type of material, the local topography of the interacting surfaces, the stress state and the mode of ...deformation. This paper examines the mechanics of a mated smooth interface that is subjected to a normal stress and where the contact is perturbed by a circular patch that can experience dilatancy under shear. The analysis of the static stress drop occurring during shear at the interface is examined using a contact mechanics approach that accounts for the separation at the pre-compressed geological interface induced by the development of dilatancy of the patch during relative shear. This paper presents an elementary model of the mechanics that takes into consideration the normal stress evolution during dilatant shearing of the interface. The problem is of particular interest to the modelling of local phenomena that can occur at material interfaces and geological faults that are subjected to steady movement.
On poro-hyperelastic shear Suvorov, A.P.; Selvadurai, A.P.S.
Journal of the mechanics and physics of solids,
November 2016, 2016-11-00, Letnik:
96
Journal Article
Recenzirano
The paper examines the problem of the shear of a porous hyperelastic material, the pore space of which is saturated with an incompressible fluid. Poro-hyperelasticity provides a suitable approach for ...modelling the mechanical behaviour of highly deformable materials in engineering applications and particularly soft tissues encountered in biomechanical applications. Unlike with the infinitesimal theory of poroelasticity, the application of pure shear generates pore fluid pressures that dissipate with time as fluid migrates either from or into the pore space due to the generated fluid pressure gradients. The analytical results provide benchmark problems that can be used to examine the accuracy of computational approaches.
In this paper, we examine the coupled thermo-poromechanical behaviour of a fluid-saturated porous medium of infinite extent bounded internally by a fluid-filled cavity. The mechanical behaviour of ...the porous skeleton can either be Hookean elastic or elasto-plastic, with a constitutive response corresponding to a modified Cam Clay plasticity model. The fluid within the cavity can be subjected simultaneously to a temperature rise and a pressure pulse. The paper presents analytical results for the spherically symmetric thermo-poroelasticity problem and these are used to validate the thermo-poroelasticity module of a computational code. We proceed to examine the thermo-poroelasto-plasticity problem. Results presented in the paper illustrate the interaction between thermal and mechanical phenomena and their influence on the cavity fluid pressure and the skeletal stresses at the cavity boundary. The paper presents solutions that will be of value in benchmarking exercises.
The paper investigates the development of instability in an internally pressurized annulus of a poro-hyperelastic material. The theory of poro-hyperelasticity is proposed as an approach for modelling ...the mechanical behaviour of highly deformable elastic materials, the pore space of which is saturated with a fluid. The consideration of coupling between the mechanical response of the hyperelastic porous skeleton and the pore fluid is important when applying the developments to soft tissues encountered in biomechanical applications. The paper examines the development of an instability in a poro-hyperelastic annulus subjected to internal pressure. Using a computational approach, numerical solutions are obtained for the internal pressures that promote either short-term or long-term instability in a poro-hyperelastic annulus and a poro-hyperelastic shell. In addition, time-dependent effects of stability loss are examined. The analytical solutions are used to benchmark the accuracy of the computational approach.
This paper examines the coupled hydro-thermo-mechanical behaviour of a fluid-saturated porous sphere with a skeletal fabric that can exhibit either elastic or elasto-plastic mechanical behaviour. ...Analytical results for the thermo-poro-elastic response of the sphere subjected to transient heat transfer are complemented by computational results for the analogous thermo-poro-elasto-plastic problem. The results presented in the paper examine the influence of the permeability, thermal expansion properties of the pore fluid and the skeleton, and the elasto-plasticity effects of the porous skeleton on the time-dependent pore fluid pressure, displacement and stress within the sphere.
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