A Topology and Geometry Sensitive Surrogate Model for Explicit Mechanics with Fracture

  • Piat, William (Safran)

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Explicit mechanics simulations are widely used to perform design optimization and safety studies, they allow to reduce the overall need for physical experiments and thus the cost of design studies. However, the recent need for probabilistic studies stresses the need for faster, cheaper rollouts. In that context it has become common practice to resort to a surrogate model - i.e. a statistical model - that learned on previous simulations to predict the outcome of a new configuration. Yet, replacing a Finite Element (FE) solver or a Finite Volume (FV) solver by a statistical model is challenging. Deep learning has been extensively used due to its success in building prediction from high dimensional input. The interest around physics statistical problem started with the first works around PINNs [1]. Operator learning [2,3] has become in the past years a privileged way for building predictive models in the context of physical simulations. This success can be attributed to two major add-ons compared to classical machine learning: on the one hand it provides dedicated architectures to perform learning on infinite dimensional spaces [4,5]. On the other hand, progress has been made on the formulation of the learning problem to add penalizing terms to introduce inductive bias in the training phase [2]. However in explicit mechanics non-linear behaviors include, plasticity, rupture or contact that traditionally benefit from dedicated, finely-tuned and solver-dependent methods. As gradients can hardly be retrieved from numerical solvers the current literature focuses on data-driven approaches resorting to large simulation databases. In this contribution we therefore address, in a purely data-driven manner, the problem of Operator Learning under geometric and topology variability for highly non-linear behavior in explicit mechanics. Our work presents promising results of an architecture that can predict fractures and especially when they occur for new geometries and topologies.