Mechanical MNIST Crack Path

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 $(G_f)$, and Failure Strength $(f_t)$ 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 $G_f$ is $2.7$, and the background value for $f_t$ 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 simulations scripts shared on GitHub. The following information is included in our dataset: (1) A rigidity ratio array to capture heterogeneous material distribution reported over a uniform $64\times64$ grid, (2) the damage field at the final level of applied displacement reported over a uniform $256\times256$ grid, and (3) the force-displacement curves for each simulation. All simulations are conducted with the FEniCS computing platform (https://fenicsproject.org). The code to reproduce these simulations is hosted on GitHub (https://github.com/saeedmhz/phase-field).