SFB 1313 publication published in "Transport in Porous Media" by Holger Steeb and Jörg Renner entitled "Mechanics of Poro-Elastic Media: A review with Emphasis on Foundational State Variables".
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.
Keywords: Poro-elasticity, Mixture Theory, Consolidation, Biot's theory, Hydromechanical coupling