中尺度位错几何形状的分布方法
A distributional approach to the geometry of dislocations at the mesoscale
摘要：
我们发展了一个理论来代表位错单晶在介观尺度上考虑集中效应，结合多值运动场的分布理论。我们的方法给出了一个新的理解的缺陷的连续介质理论，由Kroener（1980）和其他作者。基本的二维身份有关的不相容张量的弗兰克和伯格斯矢量证明在全球应变假设依赖于几何测度理论，从而产生严格的均匀化从介观到宏观尺度。
英文摘要：
We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new understanding of the continuum theory of defects as developed by Kroener (1980) and other authors. Fundamental 2D identities relating the incompatibility tensor to the Frank and Burgers vectors are proved under global strain assumptions relying on the geometric measure theory, thereby giving rise to rigorous homogenisation from mesoscopic to macroscopic scale.
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