THE CONSTITUTIVE LAW OF NONLINEAR VISCOUS AND POROUS MATERIALS

THIS PAPER examines with the help of micromechanics the overall behaviour of nonlinear viscous materials containing voids. In complement to variational bounds derived here and to several models proposed in the recent literature we derive a simple model which meets exactly a closed-form solution of a hollow sphere under hydrostatic tension. More generally we consider the problem of a hollow sphere under hydrostatic tension when the constitutive material of the sphere is already porous. The solution is used in a self-consistent scheme and a differential scheme to derive a constitutive law for a porous material containing different populations of micro-voids with distributed sizes. These schemes predict a higher damage effect for the same porosity than the models based on a single size of voids. All the models considered in this paper make use of a strain-rate potential and most of them assumme a simple "quadratic" form for it.