On thermodynamics of nonlinear poroelastic materials

The paper contains a brief presentation of a macroscopical thermodynamic model of poroelastic materials with many fluid components. A particular emphasis is placed on a Lagrangian formulation of the model and, consequently, on a consistent formulation of field equations on the reference configuration of the skeleton (solid phase of the mixture). It is demonstrated that the model possesses an identical structure as that in the pioneering work of C. A. Truesdell on the continuum mixture of fluids. An issue of porosity as an additional microstructural variable is particularly exposed

Elastic modelling of surface waves in single and multicomponent systems -- Lecture notes

The main aim of this article is to present a review of most important acoustic surface waves which are described by linear one- and two-component models. It has been written for the CISM-course: Surface waves in Geomechanics (Udine, September 6-10, 2004). Among the waves in one-component linear elastic media we present the classical Rayleigh waves on a plane boundary, Rayleigh waves on a cylindrical surface, Love waves, Stoneley waves (solid/solid and fluid/solid interface). In the second part of the article we discuss two two-component models of porous materials (Biot's model and a simple mixture model). We indicate basic differences of the models and demonstrate qualitative similarities. We introduce as well some fundamental notions yielding the description of surface waves in two-component systems (saturated porous materials) and review certain (porous materials with impermeable boundaries) asymptotic results for such waves. However, the full discussion of this subject including numerous results of computer calculations can be found in the article of B. Albers also included in this volume

Threshold to liquefaction in granular materials as a formation of strong wave discontinuity in poroelastic media

We consider a one-dimensional problem of propagation of acoustic waves in a nonlinear poroelastic saurated material. Stress-strain relations in the skeleton are described by Signorini-type constitutitve equations. Material parameters depend on the current porosity. The governing set of equations describes changes of extension of the skeleton, and of the mass density of the fluid, partial velocities of the skeleton and of the fluid and a porosity. We rely on a second order approximation. Relations of the critical time to an initial porosity and to an initial amplitude are discussed. The connection to the threshold of liquefaction in granular materials is indicated

Linear sound waves in poroelastic materials: Simple mixture vs. Biot's model

The work contains the comparison of speeds and attenuations of P1-, S-, and P2-waves in poroelastic materials obtained within Biot's model and simple mixture model

On a homogeneous adsorption in porous materials

The paper contains a proposition of a model of adsorption in porous, and granular materials. It is assumed that the mass source resulting from adsorption consists of two contributions: an equilibrium phase change described by the Langmuir isotherm, and a nonequilibrium change due to the relaxation of porosity. The model is illustrated by a simple numerical example of a homogeneous adsorption process

On a micro-macro transition for poroelastic Biot's model and corresponding Gassmann-type relations

In the paper we consider a micro-macro transition for a linear thermodynamical model of poroelastic media which yields the Biot's model. We investigate a two-component poroelastic linear model in which a constitutive dependence on the porosity gradient is incorporated and this is compared with the classical Biot's model without added mass effects. We analyze three Gedankenexperiments: jacketed undrained, jacketed drained and unjacketed and derive a generalization of classical Gassmann relations between macroscopic material parameters and microscopic compressibility moduli of the solid, and of the fluid. Dependence on the porosity is particularly exposed due to its importance in acoustic applications of the model. In particular we show that Gassmann relations follow as one of two physically justified solutions of the full set of micro-macro compatibility relations. In this solution the coupling to the porosity gradient is absent. Simultaneously, we demonstrate the second solution which lies near the Gassmann results but admits the coupling. In both models couplings are weak enough to admit, within the class of problems of acoustic wave analysis, an approximation by a "simple mixture" model in which coupling of stresses is fully neglected

On the time of existence of weak discontinuity waves in poroelastic materials

In the paper, we consider the possibility of the growth of strong discontinuity waves in the two-component poroelastic materials. We use the model with the hyperbolic set of field equations described in the paper K. Wilmanski [19961]. It is shown that indeed the critical time (i.e. the maximum time of existence of classical solutions) is finite and it assumes realistic values for real physical systems, such as biological tissues