Abstract
The plastic waves in rate-independent, isotropically work-hardening media obeying the von Mises yield condition generated by radial stress uniformly applied at a circular cavity of radius r = r0, are studied. Both plane stress and plane strain motions are considered. The radial stress and its time derivative at the cavity may be discontinuous at time t = t0. If the applied radial stress is continuous while its time derivative is not, the discontinuity at (r0, t0) propagates into r >r0 along the characteristics and/or the elastic-plastic boundaries. If the applied radial stress itself is discontinuous, the discontinuity in stress may propagate into r >r0 in the form of a shock wave, or a pseudo centered simple wave, or a combination of both. This is a systematic study on the nature of solutions in the neighborhood of (r0, t0) for all possible combinations of discontinuous loadings applied at (r0, t0). The special cases of linear work-hardening and perfectly-plastic media are also discussed. Finally, the corresponding problem for materials obeying the Tresca yield condition is studied briefly.
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