基于场位错力学的塑性力学模型问题的数值模拟
Numerical simulation of model problems in plasticity based on field dislocation mechanics
摘要：
本文的目的是研究场位错力学（FDM）理论的数值实现的模拟位错介导的塑性。首先，回顾Acharya和Roy（2006）的中尺度FDM理论，其允许在静态问题的形式下表达方程组，对应于针对给定位错密度分布的局部应力场的确定，由对应于位错密度的输运的演化问题补充。使用基于FFT的技术解决静态问题（Brenner等人，2014年）。本研究的主要贡献是一个有效的数值方案的基础上高分辨率Godunov型求解器来解决演化问题。位错介导的塑性模型问题，最后被认为是在一个简化层的情况下。首先，被认为是与均匀的速度，它允许再现湮灭的位错和位错环的膨胀的解耦问题。然后，有限差分理论被应用到位错微观结构的几个问题，受到机械载荷。
英文摘要：
The aim of this paper is to investigate the numerical implementation of the Field Dislocation Mechanics (FDM) theory for the simulation of dislocation-mediated plasticity. First, the mesoscale FDM theory of Acharya and Roy (2006) is recalled which permits to express the set of equations under the form of a static problem, corresponding to the determination of the local stress field for a given dislocation density distribution, complemented by an evolution problem, corresponding to the transport of the dislocation density. The static problem is solved using FFT-based techniques (Brenner et al., 2014). The main contribution of the present study is an efficient numerical scheme based on high resolution Godunov-type solvers to solve the evolution problem. Model problems of dislocation-mediated plasticity are finally considered in a simplified layer case. First, uncoupled problems with uniform velocity are considered, which permits to reproduce annihilation of dislocations and expansion of dislocation loops. Then, the FDM theory is applied to several problems of dislocation microstructures subjected to a mechanical loading.
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