Abstract
An uni-axial shear elastic-plastic-viscoplastic constitutive equation has been derived from the generalized constitutive equation. The constitutive equation is in which the understress in introduced to the shear strain and the overstress is employed in the shear viscoplastic strain rate. Using the constitutive equation, an analysis is done on the one-dimensional uni-axial shear elastic-plastic-viscoplastic stress wave propagation. And the equations describing the wave propagation speed and the relation of any physical quantities are derived. The derived equation for describing the shear wave propagation speed expresses the experimental results qualitatively. Also, from the developped theory of the shear elastic-plastic-viscoplastic wave propagation, the theories of a shear elastic-plastic, elastic-viscoplastic and elastic wave propagation are derived. The wave propagation speed of the elastic-viscoplastic theory can't express that of the experimental results at all except the precursor.
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