A general approach for defining the macroscopic free energy density of saturated porous media at finite strains under non-isothermal conditions

• Published in: European journal of mechanics, A, Solids Vol. 30; no. 6; pp. 1040 - 1054
• Main Author: Gajo, A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Masson SAS 01.11.2011; Elsevier
• Subjects: Compressible constituents; Computational fluid dynamics; Constituents; Density; Entropy; Exact sciences and technology; Finite strains; Fluid flow; Fluids; Free energy; Fundamental areas of phenomenology (including applications); Hyperelastic behaviour; Non-isothermal conditions; Physics; Porous media; Solid mechanics; Static elasticity (thermoelasticity...); Strain; Structural and continuum mechanics; Porous media; Finite strains; Compressible constituents; Non-isothermal conditions; Hyperelastic behaviour; Isothermal condition; Compressible fluid; High strain; Variable mass; Energy function; Enthalpy; Mixture theory; Energy density; Entropy; Porous material; Saturated porous medium; Modeling; Free energy; Hyperelasticity; Non isothermal condition; Open systems; Compressible material; Density function
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2011.06.008

A general approach is proposed for defining the macroscopic free energy density function (and its complement, the free enthalpy) of a saturated porous medium submitted to finite deformations under non-isothermal conditions, in the case of compressible fluid and solid constituents. Reference is made to an elementary volume treated as an ‘open system’, moving with the solid skeleton. The proposed free energy depends on the generalised strains (namely an appropriate measure of the strain of the solid skeleton and the variation in fluid mass content) and the absolute temperatures of the solid and fluid phases (which are assumed to differ from each other for the sake of generality). This macroscopic energy proves to be a potential for the generalised stresses (namely the associated measure of the total stress and the free enthalpy of the pore fluid per unit mass) and the entropies of the solid and fluid phases. In contrast with mixture theories, the resulting free energy is not the simple sum of the free energies of the single constituents. Two simplified cases are examined in detail, i.e. the semilinear theory (originally proposed for isothermal conditions and extended here to non-isothermal problems) and the linear theory. The proposed approach paves the way to the consistent non-isothermal-hyperelastic-plastic modelling of saturated porous media with a compressible fluid and solid constituents.