A one-dimensional field dislocation mechanics model using discontinuous Galerkin method
A one-dimensional field dislocation mechanics model using discontinuous Galerkin method
复制标题
采用间断伽辽金法的一维场位错力学模型
DOI：
10.1016/j.commatsci.2022.111870
复制
发表时间：
2023
影响因子：
3.3
通讯作者：
Puri, Saurabh
中科院分区：
文献类型：
--
作者：
Breeden, Ja’Nya;Drake, Dow;Gopalakrishnan, Jay;Puri, Saurabh
开发了一种使用不连续伽辽金 (DG) 方法的一维场位错力学 (FDM) 模型的数值求解策略。 FDM 模型能够使用偏微分方程模拟离散、非奇异位错的动力学，该方程涉及 Burgers 矢量内容的守恒定律以及成核和速度的本构输入。在这种连续弹塑性框架的背景下，对具有平衡致密核心结构的各个位错线进行建模需要非凸存储能量密度。使用基于热力学的本构定律对由位错耗散传输引起的永久变形和应力重新分布进行建模。采用 DG 方法对位错密度演化方程进行离散化，当解光滑时可产生高阶精度。讨论了使用高阶显式龙格-库塔时间步进和隐式-显式方案的权衡。开发的数值方案用于模拟非零施加应变情况下单螺位错壁的传输。
A numerical solution strategy for a one-dimensional field dislocation mechanics (FDM) model using the Discontinuous Galerkin (DG) method is developed. The FDM model is capable of simulating the dynamics of discrete, nonsingular dislocations using a partial differential equation involving a conservation law for the Burgers vector content with constitutive input for nucleation and velocity. Modeling of individual dislocation lines with an equilibrium compact core structure in the context of this continuum elastoplastic framework requires a non-convex stored energy density. Permanent deformation and stress redistribution caused by the dissipative transport of dislocations is modeled using thermodynamics-based constitutive laws. A DG method is employed to discretize the evolution equation of dislocation density yielding high orders of accuracy when the solution is smooth. The trade-offs of using a high order explicit Runge–Kutta time stepping and an implicit–explicit scheme are discussed. The developed numerical scheme is used to simulate the transport of a single screw dislocation wall in the case of a non-zero applied strain.
影响因子：
5.3
作者：
A. Acharya
通讯作者：
A. Acharya
使用时间显式龙格-库塔不连续伽辽金有限元方法进行位错传输
DOI：
10.1088/1361-651x/ac44a7
发表时间：
2021
影响因子：
1.8
作者：
M. Upadhyay;J. Bleyer
通讯作者：
J. Bleyer
DOI：
10.1098/rspa.2002.1095
发表时间：
2002
期刊：
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
影响因子：
--
作者：
A. Acharya
通讯作者：
A. Acharya