Numerical results: Finite difference approximation of nonlinear state-based peridynamic model

We share the data used in publishing the article "Numerical convergence of finite difference approximations for state based peridynamic fracture models", see https://doi.org/10.1016/j.cma.2019.03.024. The data set comprises of raw data produced by computational code, post-processed files, and python script files. We consider finite difference approximation of a nonlinear state-based peridynamic model. We run simulation for two problems. In the first problem, we have a square domain with verticle pre-crack originating from the middle of the bottom edge. We apply a constant velocity boundary condition along the horizontal axis on the bottom layer. In response to the boundary conditions, the crack propagates vertically. The data correspond to three different horizons, 2mm, 4mm, and 8mm. For each horizon, we have three results, each corresponding to mesh size horizon/2, horizon/4, and horizon/8. From the approximate displacement fields, we compute the rate of convergence with respect to mesh size, for each fixed horizon. These are post-processed data and can be found in "postprocessing" folder of Example 1. In the second problem, we consider a rectangle domain which is supported at two regions (left and right) near the bottom edge. On the portion of the top edge, we apply a monotonically increasing in time force in the downward direction. We run simulation when the sample has just one vertical pre-crack originating from the middle of the bottom edge and when the sample has two vertical pre-cracks symmetrically located and originating from the bottom edge. We plot the damage at multiple times and show that the crack propagates upwards in response to applied load. All computations are carried out using an in-house developed code. In this data set, we have not shared the computational code. However, we plan on making the code public in the future. If you are interested in our code and if you have some collaborative ideas please feel free to get in touch.

我们共享了发表于论文《基于状态近场动力学断裂模型的有限差分数值收敛性》（Numerical convergence of finite difference approximations for state based peridynamic fracture models，详见https://doi.org/10.1016/j.cma.2019.03.024）所用的数据。本数据集包含由计算程序生成的原始数据、后处理文件以及Python脚本文件。本研究针对非线性基于状态的近场动力学（peridynamic）模型开展有限差分近似分析，共设置两类仿真工况。第一类工况：计算域为正方形，底部边缘中点处带有一条垂直预制裂纹，我们在底层沿水平方向施加恒定速度边界条件，受边界条件驱动，裂纹沿垂直方向扩展。本次仿真采用2mm、4mm、8mm三种不同的视界尺寸，针对每种视界尺寸，分别得到三组仿真结果，对应网格尺寸分别为视界尺寸的1/2、1/4与1/8。基于近似位移场，我们针对每种固定视界尺寸计算了关于网格尺寸的收敛速率，该部分后处理数据可在示例1的"postprocessing"文件夹中获取。第二类工况：计算域为矩形，底部边缘附近的左右两个区域设有支撑，我们在顶部边缘的部分区域施加随时间单调递增的向下载荷。本次仿真分别针对两种预制裂纹工况开展：一种为底部边缘中点处带有一条垂直预制裂纹的试样，另一种为底部边缘处对称分布两条垂直预制裂纹的试样。我们绘制了多个时刻的损伤云图，结果表明在施加的载荷作用下，裂纹沿向上方向扩展。所有计算均采用自研程序完成，本次数据集未包含计算程序，但我们计划于未来公开该程序。若您对我们的程序感兴趣或有合作意向，欢迎随时联系我们。