Cylindrical elastic-plastic waves due to discontinuous loading at a circular cavity
Cylindrical elastic-plastic waves due to discontinuous loading at a circular cavity
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DOI：
10.1016/0020-7683(75)90048-7
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发表时间：
1975-09
影响因子：
3.6
通讯作者：
M. Srinivasan;T. Ting
中科院分区：
文献类型：
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作者：
M. Srinivasan;T. Ting
研究了径向应力均匀作用于半径r= 0的圆腔时，在速率无关、各向同性加工硬化介质中服从von Mises屈服条件的塑性波。考虑了平面应力和平面应变运动。径向应力及其在空腔处的时间导数在时间= 0时可能是不连续的。如果施加的径向应力是连续的，而其时间导数不是，则（r0,t0）处的不连续沿特征和/或弹塑性边界向>r0处传播。如果施加的径向应力本身是不连续的，则应力的不连续可能以激波或伪中心简单波的形式传播到>r0中，或两者的组合。这是对（r0,t0）处所有可能的不连续载荷组合在（r0,t0）邻域解的性质的系统研究。讨论了线性加工硬化和完全塑性介质的特殊情况。最后，对符合Tresca屈服条件的材料的相应问题进行了简要的研究。
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 radiusr=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 timet=t0. If the applied radial stress is continuous while its time derivative is not, the discontinuity at (r0,t0) propagates intor>r0along the characteristics and/or the elastic-plastic boundaries. If the applied radial stress itself is discontinuous, the discontinuity in stress may propagate intor>r0in 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.