On the constitutive potential for powder and porous bodies

This paper examines the general structure of constitutive laws for compressible bodies. Porous (sintered and ductile) bodies are considered. The simple cylindrical unit cell model is used to evaluate the rate-dependence a the constitutive law for isotropic porous bodies. The special choice of the stress-strain rate relation for the matrix material has provided the exact analytical expression for the given law which has been obtained for a wide spectrum of matrix rheological properties (from rigid plasticity to linear viscosity). It has been established that the macroscopic potential for the exact model does not exist. The connection between the condition for the existence of the macroscopic potential and the constitutive law for the matrix are considered. The rate dependence of the pressure transmission coefficient is established. The upper bound of the developed theory has a form which is inherent to creep models bared on the elliptical macroscopic potential, including the plastic behaviour.