Numerical-continuation-enhanced flexible boundary condition scheme applied to mode-I and mode-III fracture.
Numerical-continuation-enhanced flexible boundary condition scheme applied to mode-I and mode-III fracture.
复制标题
适用于 I 型和 III 型断裂的数值连续增强柔性边界条件方案。
DOI：
10.1103/physreve.103.033002
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Buze M
中科院分区：
文献类型：
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作者：
Buze M
由于使用不反映裂纹尖端运动的静态边界条件进行裂纹扩展原子模拟的不足，我们扩展了Sinclair的柔性边界条件算法[J]。E.辛克莱，Philos。并提出了一种数值连续增强的柔性边界方案，使裂缝的完整解路径可以用伪弧长连续计算，并提出了一种将更详细的远场信息纳入模型的方法，几乎没有额外的计算成本。该算法非常适合研究晶格捕获屏障脆性断裂的细节，可以纳入密度泛函理论和多尺度量子、经典量子力学和分子力学计算。我们用一个2D玩具模型展示了我们的iii型断裂方法，并利用真实的原子间电位对硅的i型断裂进行了3D研究，突出了该方法相对于采用相应的静态边界条件的优越性。特别是，数值延拓的包含使得包含几千个原子的实际模型系统能够获得收敛的结果，并且计算每个新解所需的迭代很少。我们还介绍了一种估算允许应力强度因子的晶格捕获范围的方法，并证明了它在玩具和现实模型系统上的实用性。
Motivated by the inadequacy of conducting atomistic simulations of crack propagation using static boundary conditions that do not reflect the movement of the crack tip, we extend Sinclair's flexible boundary condition algorithm [J. E. Sinclair, Philos. Mag. 31, 647 (1975)PHMAA40031-808610.1080/14786437508226544] and propose a numerical-continuation-enhanced flexible boundary scheme, enabling full solution paths for cracks to be computed with pseudo-arclength continuation, and present a method for incorporating more detailed far-field information into the model for next to no additional computational cost. The algorithms are ideally suited to study details of lattice trapping barriers to brittle fracture and can be incorporated into density functional theory and multiscale quantum and classical quantum mechanics and molecular mechanics calculations. We demonstrate our approach for mode-III fracture with a 2D toy model and employ it to conduct a 3D study of mode-I fracture of silicon using realistic interatomic potentials, highlighting the superiority of the approach over employing a corresponding static boundary condition. In particular, the inclusion of numerical continuation enables converged results to be obtained with realistic model systems containing a few thousand atoms, with very few iterations required to compute each new solution. We also introduce a method to estimate the lattice trapping range of admissible stress intensity factorsvery cheaply and demonstrate its utility on both the toy and realistic model systems.