An Elastic-Plastic-Viscoplastic Constitutive Equation

Abstract

Two main properties of the solid materials are strain rate dependence of stress and strain dependence of wave propagation speed. These phenomena are expressed by using a simple tensile elastic-plastic-viscoplastic constitutive equation in which the under-stress and over-stress are introduced. In addition, strain rate dependence of wave propagation speed is predicted by an equation derived from the above-mentioned one, describing speed of elastic-plastic-viscoplastic stress wave. Based on uni-axial elastic-plastic-viscoplastic consitutive equation, a generalized constitutive equation is proposed for the non-prestrained and non-prestressed solid materials. For the purpose of generalizing, not only under-stress and over-stress but also the third invariant of stress deviator is taken into account. Moreover, It is shown that the proposed equation includes a generalized elastic-plastic, elastic-viscoplastic and elastic constitutive equation.