A Form of An Elastic-Plastic-Viscoplastic Constitutive Equation.

Main properties of the solid materials are strain-rate dependence of stress and strain dependence of wave propagation speed. These phenomena are expressed by use of a simple tensile elastic-plastic-viscoplastic constitutive equation in which the understress and overstress are introduced. The equation describing the speed of elastic-plastic-viscoplastic stress waves predicts strain rate dependence of wave propagation speed. Based on an uni-axial elastic-plastic-viscoplastic constitutive equation, a generalized constitutive equation is proposed for the non pre-strained and non pre-stressed solid materials. For generalizing, not only the understress and the overstress are generalized but also the third invariant of the deviatoric stress tensor is considered. Moreover, It is shown that the proposed equation includes a generalized elastic-plastic, elastic-viscoplastic and elastic constitutive equation for the special cases.