The upscaling of a system of screw dislocations in a material subject to an external strain is studied. The $\Gamma$-limit of a suitable rescaling of the renormalized energy is characterized in the space of probability measures. This corresponds to a discrete-to-continuum limit of the dislocations, which, as a byproduct, provides information on their distribution when the circulation of the tangential component of the external strain becomes larger and larger. Specifically, for particular choices of the limiting external strain, dislocations are shown to concentrate at the boundary of the material and to distribute as the limiting external strain.

中文翻译：

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随着切向应变的增加，螺钉脱位的扩大

研究了受外部应变作用的材料中螺旋位错系统的升级。在概率测度的空间中表征了重新归一化的能量的适当重新定标的$ \ Gamma-极限。这对应于位错的离散到连续极限，当外部应变的切向分量的循环越来越大时，它作为副产物提供有关其分布的信息。具体而言，对于极限外部应变的特定选择，位错显示为集中在材料的边界处并作为极限外部应变分布。