WIAS Preprint No. 901, (2004)

Thermodynamics of simple two-component thermo-poroelastic media


  • Wilmanski, Krzysztof

2010 Mathematics Subject Classification

  • 80A17 74A20 74F10


  • Thermodynamics of multicomponent systems, thermo-poroelastic materials, simple mixtures


The paper is devoted to the thermodynamic construction of a two-component model of poroelastic media undergoing, in contrast to earlier works on this subject, nonisothermal processes. Under the constitutive dependence on partial mass densities, deformation gradient of skeleton, relative velocity, temperature, temperature gradient and porosity (simple poroelastic material) as well as the assumption of small deviations from the thermodynamic equilibrium we construct explicit relations for fluxes, prove the splitting of the free energy into partial contributions without mechanical couplings, construct a chemical potential for the fluid component important for the formulation of boundary conditions on permeable boundaries. We discuss as well a modification of the porosity balance equation in which we account for time changes of equilibrium porosity. This modification yields the behavior of the model characteristic for granular materials.

Appeared in

  • Trends and Applications of Mathematics to Mechanics. STAMM-2002, G. Romano, S. Rionero, eds., Springer, Wien [u.a.], 2005, pp. 293-306.

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