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Thermodynamical admissibility of Biot's model of poroelastic saturated materials

Wilmański K.

Archives of Mechanics

2002

Vol. 54, nr 5-6

709-736

The paper is devoted to the analysis of nonlinear elastic two-component models of saturated porous media, which in a linear form, reproduce as closely as possible the classical Biot's model. We present a full evaluation of the second law of thermodynamics for four classes of nonlinear models. It is proven that two of them in which there is no dependence on higher gradients cannot lead to the Biot's model. On the other hand, two other models in which a dependence on the gradient of porosity is introduced, yield linear constitutive relations but not the field equations appearing in the Biot's model. However, a recombination of partial stresses and momentum sources leads to Biot's equations. This analysis together with earlier publications on the subject exhausts the discussion of the question of thermodynamical admissibility of the Biot's model.