Mechanical MNIST - Cahn-Hilliard

The associated paper “Enhancing Mechanical Metamodels with a Generative Model-Based Augmented Training Dataset” is forthcoming. All code necessary to reproduce this dataset is available on GitHub (https://github.com/elejeune11/Mechanical-MNIST-Cahn-Hilliard). For questions, please contact Emma Lejeune (elejeune@bu.edu).The Mechanical MNIST Cahn-Hilliard dataset contains the results of 104,813 Finite Element simulations of a heterogeneous material domain subject to large equibiaxial extension deformation. The heterogeneous domain patterns are generated from a Finite Element implementation of the Cahn-Hilliard equation. Different stripe and circle patterns are obtained by varying four simulation parameters: the initial concentration, the grid size on which the concentration is initialized, parameter $\lambda$, and $b$, the peak-to-valley value of the symmetric double-well chemical free-energy function. Binary bitmap images of 400 x 400 pixels are converted into two-dimensional meshed domains of binary material using the OpenCV library, Pygmsh, and Gmsh 4.6.0. We also include in this dataset the 104,813 patterns (37,523 from case 1, 37,680 from case 2, and 29,610 from case 3) used in the Finite Element simulations stored as binary images in text files. After pattern generation, the material domain is modeled as a unit square of Neo-Hookean binary material (high concentration areas correspond to Young's Modulus 10, low concentration areas correspond to Young's Modulus 1). For equibiaxial extension, each of the four edges of the domain is displaced to 50% of the initial domain size in the direction of the outward normal to the surface with fixed displacements (d = [0.0,0.001,0.1,0.2,0.3,0.4,0.5]). Here we provide the simulation results consisting of the following: (1) change in strain energy reported at each level of applied displacement, (2) total reaction force at the four boundaries reported at each level of applied displacement, and (3) full field displacement reported at the final applied displacement d=0.5. All Finite Element simulations are conducted with the FEniCS computing platform (https://fenicsproject.org). The code to reproduce these simulations (both pattern generation simulations and equibiaxial extension simulations) is hosted on GitHub (https://github.com/elejeune11/Mechanical-MNIST-Cahn-Hilliard). The enclosed document “description.pdf'” contains additional details