Porous materials from inanimate bodies such as sand, soil and rock, living bodies such as plant tissue, animal flesh, or manmade materials can look very different due to their different origins, but as readers will see, the underlying physical. Many materials encountered in civil, geophysical and biomechanical engineering can be considered as porous media consisting. A low order finite element method for poroelasticity with. Describing a material whose solid matrix is elastic and whose fluid is viscous. The theory of linear poroelasticity describes the interaction between mechanical effects and adding or removing fluid from rock. Rice, harvard university, november 1998 revised list of references, august 2001 and april 2004, minor correctionsrewording october 2007 and april 20 for earth and planetary sciences 202, mechanics in earth and environmental sciences. The theory was proposed by maurice anthony biot 1935, 1941. Biots poroelasticity equations by homogenization springerlink. Many years ago it was suggested by professor robert e.
Poroelasticity solid mechanics at harvard university. This book treats the mechanics of porous materials infiltrated with a fluid poromechanics, focussing on its linear theory poroelasticity. Many biological tissues show timedependent, poroelastic properties arising from resistance to the fluid flow by a porous scaffold, which play important roles in their physiological functions cowin, 1999. The model builds on top of the terzaghi compaction example. An approaching train compresses the aquifer, which quickly raises the pore pressure in the affected. Pdf an introduction to linear poroelasticity researchgate. Elasticity of fluidinfiltrated porous solids poroelasticity james r. It is hypothesized that the anisotropic organization of the solid and pore volumes of cancellous bone can be physically characterized. Theory and problems of poroelasticity soil mechanics soil.
The point of departure in the description are the basic equations of elasticity i. A time domain boundary element method for poroelasticity. Poroelasticity interface biots theory for poroelasticity deformation in porous matrix due to changes in pore pressure poroelasticity uses solid mechanics and darcys law it can model anisotropic porous media if used together to solid mechanics module. For longwavelength disturbances, where h is a typical pore size propagating through a porous medium, we define average values of the local displacements in the solid and also in the saturating fluid.
Isotropic compression is the only case examined here, for. Oct 31, 2014 fluid poroelasticity defining poroelasticity. Dargush department of civil engineering, state university of new york at buffalo, buffalo, n y 14260, u. Photoelasticity definition of photoelasticity by the. This is a version of the book in pdf format, which can be read using the adobe acrobat reader.
A porous medium or a porous material is a solid often called matrix permeated by an interconnected network of pores voids filled with a fluid liquid or gas. Biot theory of poroelasticity figure 3 active pore pressures after the plastic analysis in plaxis 2d a and plaxis 3d b in which. In poroelasticity, the diffusion equation usually a electronic mail. Because parameters describing nonlinear material behavior are dif. Search for wildcards or unknown words put a in your word or phrase where you want to leave a placeholder. An e cient multigrid solver for a reformulated version of the poroelasticity system f. Exactly as we introduced a stress decomposition to define an effective stress in equation 1. Jan 28, 2010 we present here the approach to the theory of fluidfilled poroelastics based on consideration of poroelastics as a continuum of macropoints representative elementary volumes, which internal states can be described by as a set of internal parameters, such as local relative velocity of fluid and solid, density of fluid, internal strain tensor, specific area, and position of the. Assistant professorsearch for more papers by this author. Gurevich and schoenberg 1999 derive the boundary conditions directly from biots equation of poroelasticity by replacing the discontinuity surface with a thin transition layer in which the properties of the medium change rapidly but continuously and then taking the limit as the layer thickness tends to zero. In mechanics of poroelastic media the classical theory of poroelasticity developed by biot is developed and extended to the study of problems in geomechanics, biomechanics, environmental mechanics and materials science. Pdf this study is an introduction to the theory of poroelasticity expressed in terms of.
Poroelasticity is a field in materials science and mechanics that studies the interaction between fluid flow and solids deformation within a linear porous medium and it is an extension of elasticity and porous medium flow diffusion equation. For example, jaguar speed car search for an exact match put a word or phrase inside quotes. Analogous to the biot theory of soil compaction, the poroelastic properties of biological. The purpose of this contribution is to present an alternative approach to mixture theorybased poroelasticity by transferring some poroelastic concepts developed by maurice biot 1935, 1941, 1956a,b. As their name indicates, porous materials are solid structures comprised of pores or voids. Use features like bookmarks, note taking and highlighting while reading poroelasticity theory and applications of transport in porous media book 27. A large quantity of small molecules may migrate into a. As we have seen, it combines an elastic solid with pores that are filled with fluid.
Pdf this book treats the mechanics of porous materials infiltrated with a fluid. D download it once and read it on your kindle device, pc, phones or tablets. This type of material is typically associated with natural objects, such as rocks and solids, as well as biological tissues. Aeroelasticity definition of aeroelasticity by merriamwebster. The text is a standard reference for researchers interested in developing mathematical models of poroelasticity in geoenvironmental mechanics, and in the application of advanced theories of poroelastic biomaterials to the. Aeroelasticity definition is distortion as from bending in a structure such as an airplane wing or a building caused by aerodynamic forces. This type of material is typically associated with natural objects, such as rocks and solids, as well. Elasticity of fluidinfiltrated porous solids poroelasticity. Using indentation to characterize the poroelasticity of gels. Anelasticity definition and meaning collins english dictionary. The interaction between the fluid and the solid determine the overall deformation behavior of the tissue.
A derivation of the theory of linear poroelasticity. This study is an introduction to the theory of poroelasticity expressed in terms of biots theory of three. Aeroelasticity definition of aeroelasticity by merriam. When a saturated sponge is squeezed, water comes out. To solve the wave equation by direct methods, the geological model is approximated by a numerical mesh, that is, the model is discretized in a. Theory of linear poroelasticity with applications to. Poroelasticity theory and applications of transport in porous media book 27 kindle edition by cheng, alexander h. Characterizing poroelasticity of biological tissues by spherical indentation. Poromechanics is then relevant to disciplines as varied as geophysics. This version has been published for some time on the. Lecture slides molecular, cellular, and tissue biomechanics. Poroelasticity is a theory that models the interaction of deformation and fluid flow in a fluidsaturated porous medium. The poroelasticity interface couples darcys law and solid mechanics to assess deformation of porous media that results from fluid withdrawals.
Characterizing poroelasticity of biological tissues by. May 1, 2009 poroelasticity, or diffusion in elastic solids 1 poroelasticity, or diffusion in elastic solids migration of matter in an elastic solid. Wang and others published theory of linear poroelasticity find, read and cite all the research you need on researchgate. An e cient multigrid solver for a reformulated version of. Torsional wave propagation in a poroelastic hollow. Usually both solid matrix and the pore network also known as the pore. Photoelasticity definition, the phenomenon of double refraction of polarized light by a transparent substance under elastic stress, used to measure strain in elastic, transparent materials.
May 25, 2005 equations are derived whichgovern the linear macroscopic mechanical behavior of a porous elastic solid saturated with a compressible viscous fluid. Equations are derived whichgovern the linear macroscopic mechanical behavior of a porous elastic solid saturated with a compressible viscous fluid. Readings molecular, cellular, and tissue biomechanics. The word porosity is in quotes because the usual meaning of porosity is vf vcur. An improved theory for large relaxation author links open overlay panel ming wang a b c 1 liu shaobao c d 1 xu zhimin e qu kai b f li moxiao b e chen xin b e xue qing b e genin guy m. The average displacement vector for the solid frame is while that for the pore fluid is. Numerical approximation of poroelasticity with random coefficients. Poroelasticity is the term used to describe the interaction between fluid flow and solids deformation within a porous medium. The deformation of the medium influences the flow of the fluid and vice versa. As used here, the word solid refers to the skeletal framework of bulk, porous.
Poroelasticity theory and applications of transport in. A time domain boundary element method for poroelasticity g. Poroelasticity is a challenging field, but rewarding to those who make the effort to study it. This type of material is typically associated with natural objects, such as rocks. Anelasticity definition, the property of a solid in which deformation depends on the time rate of change of stress as well as on the stress itself. We present here the approach to the theory of fluidfilled poroelastics based on consideration of poroelastics as a continuum of macropoints representative elementary volumes, which internal states can be described by as a set of internal parameters, such as local relative velocity of fluid and solid, density of fluid, internal strain tensor, specific area, and. Biot problem, poroelasticity, uncertainty quantification, polynomial chaos expan sions, pseudospectral projection methods. Photoelasticity definition of photoelasticity by the free.
Theory and problems of poroelasticity 2015 verruijt a. Anelasticity definition and meaning collins english. The longterm objective of this study is facilitating the mixture modeling of biological growth phenomena. It is critical to the study of such geological phenomena as earthquakes and landslides and is important for numerous engineering projects, including dams, groundwater withdrawal, and petroleum extraction. Theory of linear poroelasticity with applications to geomechanics and hydrogeology herbert f. For the love of physics walter lewin may 16, 2011 duration. Theory and problems of poroelasticity soil mechanics. Poromechanics is a branch of physics and specifically continuum mechanics and acoustics that studies the behaviour of fluidsaturated porous media.
Department of civil engineering, state university of new york at buffalo, buffalo, n y 14260, u. Wang does an excellent job, leading the reader from basic principles to a detailed understandingwith this book you can leapfrog dozens of more arcane works and get to grips with real problems. Trabecular solid elastic and fluid transport properties the mechanical performance of cancellous bone is characterized using experiments which apply linear poroelasticity theory. Gibson to a group of colleagues to write a book on the theory of consolidation, as the theory of poroelasticity was then called, on the lines of the classical treatise by carslaw and jaeger on the conduction. Results from terzaghi compaction and biot poroelasticity analyses are compared to each other and are a good match to published analyses. The contributions are grouped into sections covering constitutive modelling, analytical aspects, numerical modelling, and applications to problems. The derivation is based on the equations of linear.
381 1510 664 372 1039 1219 664 1228 1114 414 1295 102 918 697 930 419 372 296 1224 457 1462 311 675 54 700 513 1431 1199 967 174 393 580 1406 651 1400 346 976