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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 initiatio...
330 views reported since publication in 2021.