Porous media at finite strains. The new model with the balance equation for porosity

Abstract

The purpose of this work is the presentation of the governing equations describing the two-component porous material as the mixture with the additional field of the porosity. The additional field equation for this field is proposed. The governing equations are formulated in the new Lagrangian description. The constitutive relations under arbitrary elastic deformations of the skeleton are proposed. Various simplified models and their basic properties such as the propagation of sound waves are discussed. The work should be of interest for scientists working on continuum mechanics (problems with the free boundary), on numerical methods in continuum mechanics and on the wave propagation as the method of diagnosis of media with microstructure.