Poroelasticity-I: Governing Equations of the Mechanics of Fluid-Saturated Porous Materials

Abstract

We present here the approach to the theory of fluid-filled 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 center of mass of porous space. We use the generalized CauchyBorn hypothesis and suggest that there is a system of (structural) relationships between external parameters, describing the deformation of the continuum and internal parameters, characterizing the state of representative elementary volumes. We show that in nonhomogenous (and, particularly, nonlinear) poroelastics, an interaction force between solid and fluid appears. Because this force is proportional to the gradient of porosity, absent in homogeneous poroelastics, and one can neglect with dynamics of internal degrees of freedom, this force is equivalent to the interaction force, introduced earlier by Nikolaevskiy from phenomenological reasons. At last, we show that developed theory naturally incorporates three mechanisms of energy absorption: visco-inertial Darcy mechanism, "squirt flow" attenuation, and skeleton attenuation.

Variationally consistent derivation of the stress partitioning law in saturated porous media

“…More recently, a variational approach has been adopted by Lopatnikov and Cheng (2004) and Lopatnikov and Gillespie (2010) to derive a porosity-associated additional governing equation, pairing an additional porosity field introduced as an independent state variable. A dedicated study on the problem of boundary conditions at fluid-permeable interfaces between dissimilar fluidfilled porous matrices has been reported by dell' Isola et al (2009) based on an extended Hamilton-Rayleigh principle.…”

A new approach for development of rheological relations for saturated porous media

“…Dissipation caused by chemical reactions is not included in this approach, and that is why it can hardly be applied in our case. In order to obtain rheological relations we consider that solid skeleton is elastic, then from the [5,6] we have:…”

Poroelasticity-II: On the Equilibrium State of the Fluid-Filled Penetrable Poroelastic Body

“…The theory we develop in the first paper (Lopatnikov and Gillespie 2010) is general. This means that it can be directly applied to a description of arbitrary processes in porous media.…”

“…Because we need to use results presented in the first part of this work, the references on the equation from the first part of paper (Lopatnikov and Gillespie 2010) are presented in the form (I-#). For example, the reference (I-23) refers to Eq.…”