DOI: 10.5061/dryad.rv15dv486
title: Mechanical MNIST crack path extended version

description: The Mechanical MNIST Crack Path dataset contains Finite Element simulation
 results from phase-field models of quasi-static brittle fracture in
 heterogeneous material domains subjected to prescribed loading and
 boundary conditions. For all samples, the material domain is a square with
 a side length of 1. There is an initial crack of fixed length (0.25) on
 the left edge of each domain. The bottom edge of the domain is fixed in x
 (horizontal) and y (vertical), the right edge of the domain is fixed in x
 and free in y, and the left edge is free in both x and y. The top edge is
 free in x, and in y it is displaced such that, at each step, the
 displacement increases linearly from zero at the top right corner to the
 maximum displacement on the top left corner. Maximum displacement starts
 at 0.0 and increases to 0.02 by increments of 0.0001 (200 simulation steps
 in total). The heterogeneous material distribution is obtained by adding
 rigid circular inclusions to the domain using the Fashion MNIST bitmaps as
 the reference location for the center of the inclusions. Specifically,
 each center point location is generated randomly inside a square region
 defined by the corresponding Fashion MNIST pixel when the pixel has an
 intensity value higher than 10. In addition, a minimum center-to-center
 distance limit of 0.0525 is applied while generating these center points
 for each sample. The values of Young’s Modulus (E), Fracture Toughness
 (Gf), and Failure Strength (ft) near each inclusion are increased with
 respect to the background domain by a variable rigidity ratio r. The
 background value for E is 210000, the background value for Gf is 2.7, and
 the background value for ft is 2445.42. The rigidity ratio throughout the
 domain depends on position with respect to all inclusion centers such that
 the closer a point is to the inclusion center the higher the rigidity
 ratio will be. We note that the full algorithm for constructing the
 heterogeneous material property distribution is included in the simulation
 scripts shared on GitHub. The following information is included in our
 dataset: (1) Locations of the center of the inclusions (the script to
 extract rigidity ratio matrices with the desired resolution is available
 on GitHub), (2) the displacement and damage fields every ten simulation
 step reported over a uniform 256×256 grid (3) the full resolution
 displacements and damage fields at both the final displacement step and
 the damage initiation state, and (4) the force-displacement curves for
 each simulation. All simulations are conducted with the FEniCS computing
 platform (FEniCS Project). The code to reproduce these simulations is
 hosted on GitHub (https://github.com/saeedmhz/phase-field).
description: The “Mechanical MNIST Crack Path” dataset is an addition to the
 Mechanical MNIST collection that captures crack propagation in a
 heterogeneous material. In the Mechanical MNIST Crack Path dataset, we
 model quasi-static brittle fracture in a two-dimensional heterogeneous
 material with rigid inclusions whose positions are dictated by the Fashion
 MNIST bitmap using the phase-field method, a state-of-the-art approach to
 fracture modeling. In the Mechanical MNIST Crack Path dataset, we define
 the material domain as a square with a side length of 1. There is an
 initial crack of fixed length (0.25) on the left edge of the domain. The
 bottom edge of the domain is fixed in x (horizontal), and y (vertical),
 the right edge of the domain is fixed in x and free in y, and the left
 edge is free in both x and y. The top edge is free in x, and in y it is
 displaced such that, at each step, the displacement increases linearly
 from zero at the top right corner to the maximum displacement on the top
 left corner. Maximum displacement starts at 0.0 and increases to 0.02 by
 increments of 0.0001 (200 simulation steps in total). The heterogeneous
 material distribution is obtained by adding rigid circular inclusions to
 the domain using the Fashion MNIST bitmaps as the reference location for
 the center of the inclusions. Specifically, each center point location is
 generated randomly inside a square region (a fraction of the size of the
 domain) defined by the corresponding Fashion MNIST pixel. The values of
 Young’s Modulus (E), Fracture Toughness (Gf), and Failure Strength (ft)
 near each inclusion are increased with respect to the background domain by
 a variable rigidity ratio. Note that all Finite Element simulations are
 performed in FEniCS, and all the related information and data generation
 scripts are available on GitHub. The version of this dataset hosted here
 on Dryad is the “extended version” of the Mechanical MNIST Crack Path
 dataset, which contains more information than the “lite” version hosted in
 the OpenBU Institutional Repository.
description: A list of all files included in this dataset and a short
 explanation of each file is as follows: <br> 1)
 inclusions_{test/train}.7z: Locations of the center of the inclusions
 saved as .txt files for all samples. The first column is the "x"
 coordinate, and the second column is the "y" coordinate. (the
 script to extract rigidity ratio matrices with the desired resolution is
 available on https://github.com/saeedmhz/phase-field)<br> (2)
 {damage/displacements}_low-res_{test/train}.zip: {damage/displacements}
 fields reported over a uniform 256×256 grid and recorded every ten
 simulation steps into text files with .npy format. Each file has 20 rows
 and 256×256 columns, and each row contains information of one simulation
 step.**<br> 3) {damage/displacements}_dmg-init_{test/train}.zip*:
 Full mesh resolution {damage/displacements} fields for all samples
 recorded at the early stages of damage initiation.**<br> 4)
 {damage/displacements}_last-step_{test/train}.zip*: Full mesh resolution
 {damage/displacements} fields for all samples recorded at the final step
 of the simulation.**<br> 5) force-vs-disp-{test/train}.7z: The
 reaction force in "y" direction (second column) at each maximum
 displacement (first column) is recorded in .txt files for all
 samples.<br> 6) mesh.xml: The mesh used for all
 simulations.<br> Please refer to
 https://github.com/saeedmhz/phase-field for further details and
 scripts.<br> *All files are FEniCS Functions saved as .h5 files. All
 scripts and necessary information on how to loading these files are
 available on https://github.com/saeedmhz/phase-field.<br> ** A
 folder with the name XXXX-YYYY contains information related to case #XXXX
 through case #YYYY.