Macroscopic Lagrangian formulation of poroelasticity with porosity dynamics

摘要

This paper is concerned with the theory of a fluid-filled poroelastic body. As a departure from the Biot theory, the porosity is introduced in the description of material behavior as an independent variable. Generalizing earlier work in which the equilibrium equations were obtained by means of a variational formulation, the corresponding dynamic theory is developed here. The approach leads to an interpretation of a number of physical phenomena in poroelasticity, including dynamic versus static moduli, added mass and, most importantly, porosity dynamics. Study of the dispersion relation of the second dilatational wave reveals a bifurcation in the low frequency range, and the existence of "left-handed-material" behavior between two critical frequencies in the high frequency range. We also see evidence of a third dilatational wave.