The Journal of the Acoustical Society of America · 1981 · 482 citations · 0 references
EngineeringMaterials EngineeringMaterials ScienceFluid DynamicsMechanical Behavior Of MaterialsSolid MechanicsFluid PropertiesFluid-flow In Porous MediaPorosity AnalysisPorous MaterialsPorous Media FlowTransport In Porous MediaCompressible Viscous FlowElasticityLinear Elastic BehaviorLinear ElasticityMechanical Properties Of Porous MaterialsMechanics Of Porous MediaPoroelasticityPoromechanics
The study derives equations governing the linear macroscopic mechanical behavior of a porous elastic solid saturated with a compressible viscous fluid. The derivation uses linear elasticity for the solid, linearized Navier–Stokes for the fluid, and homogenization assuming pores are small relative to the macroscopic scale. When fluid viscosity is small, the equations reduce to Biot’s form and the coefficients can be computed from microstructure; at order‑one viscosity a viscoelastic solid equation emerges.
Equations are derived which govern the linear macroscopic mechanical behavior of a porous elastic solid saturated with a compressible viscous fluid. The derivation is based on the equations of linear elasticity in the solid, the linearized Navier–Stokes equations in the fluid, and appropriate conditions at the solid–fluid boundary. The scale of the pores is assumed to be small compared to the macroscopic scale, so that the two-space method of homogenization can be used to deduce the macroscopic equations. When the dimensionless viscosity of the fluid is small, the resulting equations are those of Biot, who obtained them by hypothesizing the form of the macroscopic constitutive relations. The present derivation verifies those relations, and shows how the coefficients in them can be calculated, in principle, from the microstructure. When the dimensionless viscosity is of order one, a different equation is obtained, which is that of a viscoelastic solid.