Study On General Solution For Porous Media Multi-field Coupling

Porous media is a complex material which includes some differentsubstance, such as rock, soil etc. Because of the complexity of the microscopicstructure, the macroscopic properties exhibit complex multi-physics field couplingeffect, such as the fluid-solid coupling effect, fluid-solid-thermo coupling effect andso on. In this paper, by using of research thought for general solution ofmathematical elasticity, the general solution and refined theory of porous media andthermoporoelastic material are derived.For axisymmetric porous media，According to the constitutive equations andbalance equations which stress field satisfied, the P-N general solution ofaxisymmetric porous media is obtained by using of basic mathematical method. Andthe completeness of P-N general solution is proved. Then the Boussinesq generalsolution and Timpe general solution are obtained from P-N General Solution. At last,the solution for the circular plate under pure bending is derived.For thermoporoelastic material, According to the constitutive equations andbalance equations, the isotropic thermoporoelastic material steady-state solution inthe domain of z-convex is obtained by using Lur’e method and Almansi’s theory.And the completeness of general solution is proved. Moreover, the general solutionprovides reliable basis for engineering application. Using the same research method,the2D steady-state general solution of transversely isotropic thermoporoelasticmaterial is derived. Without any additional assumptions, the refined theory anddecomposed theorem of thermoporoelastic material are derived by using thethermoporoelastic general solution and Lur’e method. Under the homogenousboundary conditions, the decomposed theorem of thermoporoelastic material isderived. The stress state of thermoporoelastic material consists of the interior state,the transcendental state, the pore pressure state and the thermal state. Under thenon-homogenous boundary conditions, the approximate equations and solutions forthe plate are derived directly from the refined theory.