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首页> 外文期刊>SIAM Journal on Mathematical Analysis >Elastic energy stored in a crystal induced by screw dislocations: From discrete to continuous
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Elastic energy stored in a crystal induced by screw dislocations: From discrete to continuous

机译：螺杆位错引起的晶体中存储的弹性能：从离散到连续

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This paper deals with the passage from discrete to continuous in modeling the static elastic properties of vertical screw dislocations in a cylindrical crystal, in the setting of antiplanar linear elasticity. We study, in the framework of Gamma- convergence, the asymptotic behavior of the elastic stored energy induced by dislocations as the atomic scale e tends to zero, in the regime of dilute dislocations, i. e., rescaling the energy functionals by 1/epsilon(2)vertical bar log epsilon vertical bar. First we consider a continuum model, where the atomic scale is introduced as an internal scale, usually called core radius. Then we focus on a purely discrete model. In both cases, we prove that the asymptotic elastic energy as epsilon -> 0 is essentially given by the number of dislocations present in the crystal. More precisely the energy per unit volume is proportional to the length of the dislocation lines, so that our result recovers in the limit as epsilon -> 0, a line tension model.
机译：本文在反平面线性弹性的设置中，处理了从离散到连续的过程，以建模圆柱晶体中垂直螺钉位错的静态弹性特性。我们在伽马会聚的框架内研究了在位错稀疏状态下，随着原子尺度e趋于零，由位错引起的弹性储能的渐近行为。例如，按1 / epsilon（2）垂直条对数epsilon垂直条重新缩放能量功能。首先，我们考虑一个连续模型，其中原子尺度作为内部尺度引入，通常称为核半径。然后，我们关注纯离散模型。在这两种情况下，我们证明渐近弹性能为ε-> 0本质上是由晶体中存在的位错数给出的。更准确地说，每单位体积的能量与位错线的长度成正比，因此我们的结果将恢复为极限ε-> 0（线张力模型）。

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