Mechanical MNIST - Equibiaxial Extension

Abstract

Each dataset in the Mechanical MNIST collection contains the results of 70,000 (60,000 training examples + 10,000 test examples) finite element simulation of a heterogeneous material subject to large deformation. Mechanical MNIST is generated by first converting the MNIST bitmap images (http://www.pymvpa.org/datadb/mnist.html) to 2D heterogeneous blocks of material. Consistent with the MNIST bitmap ($28 \times 28$ pixels), the material domain is a $28 \times 28$ unit square. In "Mechanical MNIST - Equibiaxial Extension," the material is Neo-Hookean with a varying modulus. The top of the domain is free horizontally and moved vertically to a set of given fixed displacements (d = [0.0, 0.0005, 0.005, 0.05, 0.25, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ]), the right of the domain is free vertically and moved horizontally to a set of given fixed displacements (d = [0.0, 0.0005, 0.005, 0.05, 0.25, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ]), the bottom of the domain is free horizontally and moved vertically to a set of given fixed displacements (d = [-0.0, -0.0005, -0.005, -0.05, -0.25, -0.5, -1.0, -2.0, -3.0, -4.0, -5.0, -6.0, -7.0 ]), and the left of the domain is free vertically and moved horizontally to a set of given fixed displacements (d = [-0.0, -0.0005, -0.005, -0.05, -0.25, -0.5, -1.0, -2.0, -3.0, -4.0, -5.0, -6.0, -7.0 ]). The results of the simulations include: (1) change in strain energy at each step, (2) total reaction force at the top and right boundaries at each step, and (3) full field displacement at each step. 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/elejeune11/Mechanical-MNIST/tree/master/generate_dataset).