From dislocation motion to an additive velocity gradient decomposition, and some simple models of dislocation dynamics
From dislocation motion to an additive velocity gradient decomposition, and some simple models of dislocation dynamics
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从位错运动到加性速度梯度分解，以及位错动力学的一些简单模型
DOI：
10.1007/s11401-015-0970-0
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Xiaohan Zhang
中科院分区：
文献类型：
--
作者：
A. Acharya;Xiaohan Zhang
回顾了非约束几何非线性和材料非线性的含时位错力学的数学理论。在“小变形”的设置，一套简化的和有趣的模型组成的非局部Ginzburg朗道方程，一个非局部水平集方程，和一个非局部广义Burgers方程。在有限变形设置中，它示出的总速度梯度的添加剂分解成弹性和塑性部分自然出现从微观力学的起点，不涉及塑性变形的概念，但只有弹性变形，材料的速度，位错密度和位错速度。此外，塑性自旋张量也会自然出现。
A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a “small deformation” setting, a suite of simplified and interesting models consisting of a nonlocal Ginzburg Landau equation, a nonlocal level set equation, and a nonlocal generalized Burgers equation is derived. In the finite deformation setting, it is shown that an additive decomposition of the total velocity gradient into elastic and plastic parts emerges naturally from a micromechanical starting point that involves no notion of plastic deformation but only the elastic distortion, material velocity, dislocation density and the dislocation velocity. Moreover, a plastic spin tensor emerges naturally as well.