On Biot-like models and micro-macro transitions for poroelastic materials
- Wilmanski, Krzysztof
2010 Mathematics Subject Classification
- 80A17 74A20 74F10
- Thermodynamics, Biot's model, poroelastic materials, Gassmann relations
The paper is devoted to the thermodynamic derivation of a two-component poroelastic model with balance equation of porosity as a prototype of Biot's model. It is shown that a constitutive dependence on the porosity gradient yields the possibility of the construction of the linear Biot's model of poroelastic materials provided one negelcts the relaxation of porosity. A procedure of micro-macrotransition for a homogeneous microstructure yields Gassmann relations as an approximation of the thermodynamic model. Simultaneously it is shown that the model with the porosity balance equation can be applied to porous materials with a rather rigid skeleton. In the case of soft granular materials there exists a correction to porosity changes which follow from an appropriate modification of the porosity source.