Variational formulation of fluid infiltrated porous materials and physically-based micromechanical material constants

摘要

The constitutive behavior of a fluid infiltrated porous material is investigated by applying vari-ational principle to the Helmholtz free energy associated with the solid and fluid phases. Assuming linear response for the phase materials, the free energy is expressed in terms of quadratic forms. The volumetric deformation is characterized by four independent material constants: bulk modulus of the solid phase K_s, of the fluid phase K_f, of the porosity K_Φ, and that due to solid-porosity interaction K_ψ. Even though the phase materials are linear, the macroscopic constitutive laws are nonlinear due to the geometric nonlinearity of pore deformation. The fully linearized model is consistent with the Biot model. The quadratic energy from also allows us to examine the material stability criteria.