线弹性-理想塑性材料的准静态演化问题
Quasistatic evolution problems for linearly elastic - perfectly plastic materials
摘要：
在率无关过程变分理论的框架下，研究了小应变关联弹塑性的准静态演化问题。通过在有界变形函数空间中使用增量变分问题证明了解的存在性。这提供了一个新的近似结果的解决方案的准静态发展问题，这是绝对连续的时间。导出了速率形式问题的四种等价形式。通过引入塑性应变奇异集上应力的精确定义，得到了流动法则的一个强公式。
英文摘要：
The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain.
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