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

Published: 26 March 2019| Version 1 | DOI: 10.17632/y76rh3r8dm.1


We share the data used in publishing the article "Numerical convergence of finite difference approximations for state based peridynamic fracture models", see 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.



Louisiana State University


Numerical Analysis, Finite Difference Methods, Fracture