Convergence of Interaction-Driven Evolutions of Dislocations with Wasserstein Dissipation and Slip-Plane Confinement
Convergence of Interaction-Driven Evolutions of Dislocations with Wasserstein Dissipation and Slip-Plane Confinement
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相互作用驱动的位错演化与 Wasserstein 耗散和滑移面限制的收敛
DOI：
10.1137/16m1096098
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
L. Scardia
中科院分区：
文献类型：
--
作者：
M. G. Mora;M. Peletier;L. Scardia
我们考虑由二维域中的点表示的单滑移系统中由$n$平行的边缘位错组成的系统；弹性介质被建模为连续介质。我们用位错的经验度量来表示这个系统的能量，并证明了几个极限收敛的结果。本文的主要目的是研究经验度量的演化的收敛问题。我们考虑与速率无关的准静态演化，其中位错的运动被限制在相同的滑移面上。这导致了准静态演化问题的一种修正的沃瑟斯坦距离的表述，该距离只有在运输计划是滑移平面受限时才是有限的。由于焦点是位错之间的相互作用，我们重新正规化弹性能量，以消除潜在的大的自能或核心能。我们证明了这种重整化能量的Gamma-收敛，并构造了联合恢复序列。
We consider systems of $n$ parallel edge dislocations in a single slip system, represented by points in a two-dimensional domain; the elastic medium is modeled as a continuum. We formulate the energy of this system in terms of the empirical measure of the dislocations and prove several convergence results in the limit $n\to\infty$. The main aim of the paper is to study the convergence of the evolution of the empirical measure as $n\to\infty$. We consider rate-independent, quasi-static evolutions, in which the motion of the dislocations is restricted to the same slip plane. This leads to a formulation of the quasi-static evolution problem in terms of a modified Wasserstein distance, which is only finite when the transport plan is slip-plane-confined. Since the focus is on interaction between dislocations, we renormalize the elastic energy to remove the potentially large self- or core energy. We prove Gamma-convergence of this renormalized energy, and we construct joint recovery sequences for which both the...
DOI：
10.1007/s00526-007-0119-4
发表时间：
2008-03
影响因子：
2.1
作者：
A. Mielke;T. Roubíček;U. Stefanelli
通讯作者：
A. Mielke;T. Roubíček;U. Stefanelli