Dimensionality reduction through convolutional autoencoders for fracture patterns prediction

Dimensionality reduction methods construct a low dimensional or reduced space. Complex structural mechanics problems can be approximated on a low dimensional space with a Reduced-Order Model or surrogate model. For instance, Principal Components Analysis can compute a reduced basis from a database of full-order snapshots. Principal Components Analysis, however, does not reconstruct low dimensional spaces efficiently for highly nonlinear problems, mainly because it is a linear dimensionality reduction method. In this paper, an original approach based on an autoencoder neural network is developed to construct a nonlinear Reduced-Order Model for a highly nonlinear brittle fracture problem. We show on a set of simulations how the autoencoder can be efficient for dimensionality reduction or compression of highly nonlinear data. A complete deep learning framework is proposed to predict crack propagation patterns directly from the loading conditions. Finally, we validate our nonlinear Reduced-Order Model with data sets generated for two problems using proportional and non-proportional loading conditions. In the first problem, the crack always initiates at the same location but propagates in various directions, which may even vary during the simulation if loading conditions are non-proportional. In the second problem, the crack may additionally initiate at various locations. Results for the two problems evaluate the capabilities of the proposed approach.