Abstract
Mixture theory provides a continuum framework to model a multi-phase system. The basic assumption is, at any instant of time all phases are present at every material point and momentum and mass balance equations are postulated. This paper reviews the recent developments in mixture theory and focuses on the applications of the theory in particular areas of biomechanics, composite manufacturing and infiltration into deformable porous materials. The complexity based upon different permeability and stress functions is also addressed. The review covers the literature presented in the past fifty years and summarizes applications of mixture theory in specific areas of interest, for the sake of brevity, only necessary details are provided rather than complete modeling and simulation.
Highlights
The deformation of the porous material due to fluid flow brings changes in physical properties such as permeability and porosity of the material
The principals of modern mixture theory by using the continuum mechanics and proposing balance equations appropriate to mixtures irrespective of their constitution are formulated by Truesdell and Toupin [2], Truesdell [3,4] and Truesdell and
The main focus of the present paper to present a review of the work done after 1976, while special emphases is given on the applications of mixture theory in deformable materials
Summary
The deformation of the porous material due to fluid flow brings changes in physical properties such as permeability and porosity of the material. Biot [8] studied the problem of soil consolidation where Darcy’s law was used to describe the fluid flow coupled with linear elasticity model for solid deformation. This paved the path for further work of Biot [9,10], used extensively in soil mechanics.
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