论文标题
弹性阈值的界限，即耗散应变梯度可塑性问题
Bounds on the elastic threshold for problems of dissipative strain-gradient plasticity
论文作者
论文摘要
这项工作涉及纯粹的耗散版本，即构成速率无关的应变梯度可塑性模型。在传统的可塑性理论中，确定塑性流的方法是局部的，并且基于体内的应力分布。对于应变梯度可塑性的耗散问题，这种方法无效，因为产量函数取决于弹性区域中未知的显微压力。取而代之的是，必须在全球范围内考虑产量和塑料流。这项工作解决了通过制定全球问题的原始版和双重版本来确定弹性阈值的问题，并由极限分析中用于完美可塑性的技术动机，为阈值建立了上限和上限的条件。一般方法应用于两个示例：平面应力下的板，并受到规定的位移；并受到扭转的杠铃。
This work is concerned with the purely dissipative version of a well-established model of rate-independent strain-gradient plasticity. In the conventional theory of plasticity the approach to determining plastic flow is local, and based on the stress distribution in the body. For the dissipative problem of strain-gradient plasticity such an approach is not valid as the yield function depends on microstresses that are not known in the elastic region. Instead, yield and plastic flow must be considered at the global level. This work addresses the problem of determining the elastic threshold by formulating primal and dual versions of the global problem and, motivated by techniques used in limit analysis for perfect plasticity, establishing conditions for lower and upper bounds to the threshold. The general approach is applied to two examples: of a plate under plane stress, and subjected to a prescribed displacement; and of a bar subjected to torsion.
