Acceleration waves, flutter instabilities and stationary discontinuities in inelastic porous media

Abstract

coupled constitutive equations for a saturated porous medium are developed in the frame of the theories of mixtures : the fluid constituent is elastic and the solid skeleton behaves as a rate-independent elastic-plastic solid. Then the existence of real acceleration wave-speeds is considered : actually the analysis centers on the modes in which these wave-speeds cease to be real. An explicit criterion indicating the critical value of the plastic modulus at the onset of a stationary discontinuity (one wave-speed is zero) is derived in both cases where the fluid and solid constituents are compressible and where they are not. Furthermore, it is shown that in some circumstances, some wave-speeds cease to be real in the very early stages of the inelastic deformation process due to the incipience of a flutter instability (two wave-speeds are complex conjugate). When it is not excluded, this mode of loss of hyperbolicity of the dynamic equilibrium equations usually precedes the onset of a stationary discontinuity and may occur right at the inception of plastic loading, that is for an infinitely large plastic modulus. Flutter instability is excluded when the plastic behavior of the solid skeleton is associative and its existence depends strongly on the relative positions of the shear and longitudinal elastic wave-speeds. It is not likely to occur if the shear wave-speed is the smallest elastic wave-speed and then a stationary discontinuity prevails.