Alternative formulations of isotropic hardening for Mises materials, and associated variational inequalities
Alternative formulations of isotropic hardening for Mises materials, and associated variational inequalities
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Mises 材料各向同性硬化的替代公式以及相关的变分不等式
DOI：
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发表时间：
2009
期刊：
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通讯作者：
B. Reddy
中科院分区：
文献类型：
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作者：
M. Gurtin;B. Reddy
这项工作提供了洞察方面的经典Mises-Hill塑性，其扩展到Aifantis理论的梯度塑性，和制剂的两个理论作为变分不等式。首先，它表明，经典的各向同性硬化规则，这是耗散的性质，同样可以通过缺陷能量的特点，什么是惊人的，这个能量为基础的硬化规则模仿耗散行为描述加载过程是不可逆的。第二个方面涉及到传统形式的流动规则和它的公式在耗散方面的等价性。先前已经使用凸分析的工具建立了这种等价性（参见，例如，在一个实施例中，Han和Reddy，Plasticity：数学理论和数值分析，Springer，纽约，1999）-在当前的工作中，这种等效性直接从本构方程和耗散的特定形式导出，而不求助于这种机械。相应的耗散和能量形式的流动规则的变分不等式推导出，这些不等式只涉及位移和塑性应变，非常适合于计算研究。最后，它表明，该框架开发的经典理论很容易扩展到包含梯度塑性理论的Aifantis（跨ASME J工程材料技术106：326-330，1984）。
This work provides insight into aspects of classical Mises–Hill plasticity, its extension to the Aifantis theory of gradient plasticity, and the formulations of both theories as variational inequalities. Firstly, it is shown that the classical isotropic hardening rule, which is dissipative in nature, may equally well be characterized via a defect energy—and, what is striking, this energetically based hardening rule mimics dissipative behavior by describing loading processes that are irreversible. A second aspect concerns the equivalence between the conventional form of the flow rule and its formulation in terms of dissipation. This equivalence has been previously established using the tools of convex analysis (cf., e.g., Han and Reddy, Plasticity: mathematical theory and numerical analysis, Springer, New York, 1999)—in the current work this equivalence is derived directly from the constitutive equations and the specific form of the dissipation, without recourse to such machinery. Variational inequalities corresponding to the dissipative and energetic forms of the flow rule are derived; these inequalities involve only the displacement and plastic strain and are well suited to computational studies. Finally, it is shown that the framework developed for the classical theory is easily extended to incorporate the gradient-plasticity theory of Aifantis (Trans ASME J Eng Mater Technol 106:326–330, 1984).