HU Ya-yuan. Study on the Super Viscoelastic Constitutive Theory for Saturated Porous Media[J]. Applied Mathematics and Mechanics, 2016, 37(6): 584-598. doi: 10.3879/j.issn.1000-0887.2016.06.004
Citation: HU Ya-yuan. Study on the Super Viscoelastic Constitutive Theory for Saturated Porous Media[J]. Applied Mathematics and Mechanics, 2016, 37(6): 584-598. doi: 10.3879/j.issn.1000-0887.2016.06.004

Study on the Super Viscoelastic Constitutive Theory for Saturated Porous Media

doi: 10.3879/j.issn.1000-0887.2016.06.004
Funds:  The National Natural Science Foundation of China(51178419)
  • Received Date: 2015-11-24
  • Rev Recd Date: 2016-02-23
  • Publish Date: 2016-06-15
  • In order to establish the super viscoelastic constitutive framework for saturated porous media in view of the reversible and irreversible deformations of solids, porous solids and fluids, an energy balance equation of which all terms were in the thermodynamically power-conjugated form, was built for saturated porous media according to the principle of homogeneous mixture response, with the porous solid selected as the reference configuration and the effective stress tensor, the material’s real hydrostatic stress and the fluid’s real pore pressure chosen as the state variables. The entropy flux and entropy production of the saturated porous medium were derived based on the decomposing principle of entropy in the non-equilibrium thermodynamics. The work shows that the super elastoplastic constitutive theory is only a special case of the proposed theory. The deformation rate of a porous solid is composed of 2 parts: the solid-phase interstice and the material deformation, of which the former is power-conjugated with the Terzaghi effective stress tensor and the latter with the material’s real hydrostatic stress. The free energy of a saturated porous medium consists of 2 parts: the porous solid-phase part and the fluid-phase part. If the solid-phase interstice is decoupled from the material deformation, the free energy of the solid can be further divided into 2 parts: the material strain and the interstitial change. The Skempton-type effective stress is proved not to be a basic state variable for saturated porous media.
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