Hamiltonian/Stroh formalism for reversible poroelasticity (and thermoelasticity)

Stroh's sextic formalism represents the equilibrium equations of anisotropic elasticity in a particularly attractive form, that is most suitable for studying interface-dominated multilayered solids, composite materials and time-harmonic problems. Taking advantage of the fact that the Stroh formalism really amounts to the canonical form of the equations in the Hamiltonian sense, the case of Biot's reversible (i.e. no fluid dissipation) poroelasticity is here addressed, in the absence of a fluid pressure gradient. This framework is the same as thermoelasticity of perfect conductors. Two Hamiltonian formulations are developed: the first describes both the solid and the fluid phases and it exhibits, besides energy conservation, momentum conservation, as a result of pressure uniformity (perfectly drained conditions). The second is restricted to the solid skeleton and perfectly parallels anisotropic elasticity, where the Stroh matrices refer to the effective stress tensor. The case of weak fluid–solid coupling is also considered and it produces a perturbation from anisotropic elasticity with the same structure as incompressibility, although in an “opposing” manner. This comparison suggests that the incompressibility limit introduced by Biot should be revised. The energy conservation integral and the edge impedance matrix are also illustrated.