Abstract
A study of the instantaneous and delayed behavior of a double shear perturbation superimposed on an equilibrium state of an isotropic incompressible medium with internal variables is presented. Elastic media with general internal variables and true viscoplastic media where an intermediate configuration and particular internal parameters are chosen, are successively considered. In both cases, conditions on evolution laws and free energy are proposed, and proved to be sufficient to obtain a stable system of differential equations for the perturbations. As a consequence, the two delayed wave speeds are then real and less than or equal to the instantaneous elastic wave speeds. When the equilibrium state lies on a viscoplastic yield surface, delayed wave speeds and loading conditions may be identified with those we obtain in a plastically deforming (rate-independent) medium, with the same surface as a plastic yield surface. The signification of the relaxation time introduced is also discussed.
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