Poromechanics

Poromechanics is a branch of physics and specifically continuum mechanics and acoustics that studies the behaviour of fluid-saturated porous media. A porous medium or a porous material is a solid (often called matrix) permeated by an interconnected network of pores (voids) filled with a fluid (liquid or gas). Usually both solid matrix and the pore network (also known as the pore space) are assumed to be continuous, so as to form two interpenetrating continua such as in a sponge. Many natural substances such as rocks, soils, biological tissues, and man made materials such as foams and ceramics can be considered as porous media. Porous media whose solid matrix is elastic and the fluid is viscous are called poroelastic. A poroelastic medium is characterised by its porosity, permeability as well as the properties of its constituents (solid matrix and fluid).

The concept of a porous medium originally emerged in soil mechanics, and in particular in the works of Karl von Terzaghi, the father of soil mechanics. However a more general concept of a poroelastic medium, independent of its nature or application, is usually attributed to Maurice Anthony Biot (1905–1985), a Belgian-American engineer. In a series of papers published between 1935 and 1957 Biot developed the theory of dynamic poroelasticity (now known as Biot theory) which gives a complete and general description of the mechanical behaviour of a poroelastic medium. Biot's equations of the linear theory of poroelasticity are derived from

• Equations of linear elasticity for the solid matrix,
• Navier–Stokes equations for the viscous fluid, and
• Darcy's law for the flow of fluid through the porous matrix.

One of the key findings of the theory of poroelasticity is that in poroelastic media there exist three types of elastic waves: a shear or transverse wave, and two types of longitudinal or compressional waves, which Biot called type I and type II waves. The transverse and type I (or fast) longitudinal wave are similar to the transverse and longitudinal waves in an elastic solid, respectively. The slow compressional wave, (also known as Biot’s slow wave) is unique to poroelastic materials. The prediction of the Biot’s slow wave generated some controversy, until it was experimentally observed by Thomas Plona in 1980. Other important early contributors to the theory of poroelasticity were Yakov Frenkel and Fritz Gassmann.

Conversion of energy from fast compressional and shear waves into the highly attenuating slow compressional wave is a significant cause of elastic wave attenuation in porous media.

Recent applications of poroelasticity to biology such as modeling of blood flows through the beating myocardium have also required an extension of the equations to nonlinear (large deformation) elasticity and the inclusion of inertia forces.