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.

本数据集包含发表文章《基于状态的周期性断裂模型有限差分近似数值收敛性》所使用的原始数据，详见https://doi.org/10.1016/j.cma.2019.03.024。该数据集由计算代码生成的原始数据、后处理文件以及Python脚本文件组成。本研究考虑了非线性基于状态的周期性模型有限差分近似。针对两个问题进行了模拟。在第一个问题中，我们有一个以底边中点为起点的垂直预裂纹的正方形域。在底部层沿水平轴施加恒定速度边界条件。在边界条件的响应下，裂纹垂直扩展。数据对应于三个不同的水平面，即2mm、4mm和8mm。对于每个水平面，我们有三个结果，分别对应于网格尺寸为水平面的一半、四分之一和八分之一。从近似位移场中，我们计算了相对于网格尺寸的收敛率，对于每个固定的水平面。这些是后处理数据，可在示例1的“postprocessing”文件夹中找到。在第二个问题中，我们考虑了一个矩形域，该域在底部边缘的两侧受到支撑。在顶部边缘的一部分，我们施加了随时间单调增加的向下方向力。在样本仅有一个垂直预裂纹（从底部边缘中点起源）以及样本有两个对称位于底部边缘的垂直预裂纹的情况下进行了模拟。我们绘制了不同时间点的损伤情况，并展示了裂纹在施加的载荷作用下向上扩展。所有计算均使用内部开发的代码完成。在本数据集中，我们没有共享计算代码。然而，我们计划在未来公开代码。如果您对我们的代码感兴趣，或者如果您有任何合作想法，请随时与我们联系。