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The Volume Fraction Concept in the Porous Media Theory
Author(s) -
Bluhm J.,
De Boer R.
Publication year - 1997
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19970770803
Subject(s) - volume (thermodynamics) , porous medium , multiplicative function , volume fraction , porosity , mathematics , materials science , thermodynamics , physics , mathematical analysis , composite material
In this paper the volume fraction concept in the porous media theory is considered. First, the historical development of this important concept is traced. Thereupon, the concept of volume fractions is formulated and the transport theorems, which govern the transformations of volume elements from one placement to another, are derived. An essential feature is the incorporation of the effect of incompressibility into the transport theorems. This is only possible by the introduction of a new multiplicative decomposition of the deformation gradients of the constituents into parts describing the deformations of the realistic (true) materials and parts including the changes of the pores.