An elastoplastic theory of dislocations as a physical field theory with torsion
An elastoplastic theory of dislocations as a physical field theory with torsion
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DOI：
10.1088/0305-4470/35/8/313
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发表时间：
2001-05
期刊：
影响因子：
--
通讯作者：
M. Lazar
中科院分区：
文献类型：
--
作者：
M. Lazar
本文将各向异性或各向同性弹塑性材料中具有矩应力的位错的静态理论看作T（3）规范理论。我们得到的杨米尔斯型场方程表示的力和力矩平衡。此外，我们还讨论了位错密度与弯矩应力之间的几种本构关系。对于直螺型位错，由于力矩应力的出现，位错核附近的应力场发生了变化。首次在此框架下计算了螺型位错的局部矩应力、Nye张量、弹塑性能和修正Peach-Koehler力。此外，我们还讨论了螺位错和磁涡旋之间的直接类比。固体中的位错理论也被认为是三维有效引力理论。
We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastic material as a T(3) gauge theory. We obtain Yang-Mills-type field equations which express the force and the moment equilibrium. Additionally, we discuss several constitutive laws between the dislocation density and the moment stress. For a straight screw dislocation, we find the stress field which is modified near the dislocation core due to the appearance of moment stress. For the first time, we calculate the localized moment stress, the Nye tensor, the elastoplastic energy and the modified Peach-Koehler force of a screw dislocation in this framework. Moreover, we discuss the straightforward analogy between a screw dislocation and a magnetic vortex. The dislocation theory in solids is also considered as a three-dimensional effective theory of gravity.