Plastic wave speeds in materials whose elastic response is linear and isotropic while the plastic flow is incompressible and isotropically work-hardening are obtained. One of the three plastic wave speeds is identical to the elastic shear wave speed regardless of the form of the yield condition. The other two plastic wave speeds, cf and cs, are determined for materials obeying the von Mises yield condition. The dependence of cf and cs on the stress state and the direction of propagation is investigated in detail. The largest and smallest cf and cs, and the directions along which they occur are also presented. For materials obeying the Tresca’s yield condition, it is shown that one can obtain the corresponding results by simply specializing the results for the von Mises materials. Unlike in one-dimensional analyses where the plastic wave speed becomes zero for perfectly plastic solids, the three-dimensional analyses show that the ratio of cf to c1, where c1 is the elastic dilatation wave speed, is always larger than $3/7$ for the von Mises materials and $1/2$ for the Tresca’s materials. For most materials under moderate loadings, this ratio is much higher.

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