Abstract
We review fundamental aspects of linear poro-elasticity. In contrast to most available textbooks and review articles, our treatment of poro-elastic media is based on the continuum Mixture Theory. Kinematic state variables and dynamic variables are introduced and formally linearized before the fundamental constitutive relations, between pairs of these, are extensively discussed. The role of porosity in linear poro-elasticity is highlighted, and it is shown that porosity is one of the possible choices for one of the two kinematic state variables, and therefore, relations to alternative pairs of kinematic variables can be formulated. The treatment is concluded by the formulation of the governing set of partial differential equations that constitute the basis for analytical or numerical investigations of boundary value problems.
Highlights
Poro-elasticity is the branch of mechanics that covers the reversible deformation of aggregates composed of a solid, assumed to behave linearly elastic, and a viscous and compressible fluid or several fluids, where we consider the term fluid to comprise liquids and gases
We find that Mixture Theory provides a framework for a rather rigorous development of the theory starting from the axioms of mechanics, the conservation laws for mass and momentum
The basic conservation laws for mass and momentum take on specific forms for poro-elastic media resulting in a set of coupled partial differential equations (PDEs) that govern their isothermal deformation
Summary
Poro-elasticity is the branch of mechanics that covers the reversible deformation of aggregates composed of a solid, assumed to behave linearly elastic, and a viscous and compressible fluid or several fluids, where we consider the term fluid to comprise liquids and gases The composition of such mixtures is conventionally described by the volumetric fractions of the constituting phases, and most of the time we use porosity as a quantification of the volume fraction not occupied by solid constituents. The manuscript is organized as follows: After introducing the basic notions of Mixture Theory as applied to poro-elasticity, we discuss the partial balance equations for mass and momentum of both phases and introduce the related balance relations of the mixture These balance relations are first treated in the most general global form and initially include nonlinearities, e.g., related to the material time derivatives. When introducing the constitutive relations linking the kinematic and dynamic variables, we put emphasis on clarifying the role of porosity as kinematic state variable
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