One-Dimensional Theory of Elastic-Plastic-Viscoplastic Stress Waves of Solids in Uniaxial Stress State at Eulerian Coordinate.

Abstract

An elastic-plastic-viscoplastic constitutive equation has been proposed in which the understress is introduced to the plastic strain and the overstress is employed for the viscoplastic strain. The constitutive equation has a form in which the inelastic strain component is consists of steady and unsteady component. Using the equation, an analysis on the one-dimensional wave propagation in the uniaxial stress state at the spacial coordinate is done by the characteristic method. As the results, equations describing the wave propagation speed and the relation of the every physical quantities in Eulerian coordinate. Also, it is shown that the theories are derived of an elastic-plastic, elastic-viscoplastic and longitudinal elastic wave propagation in Eulerian coordinate from that of the developped elastic-plastic-viscoplastic wave propagation.