Learning elastoplasticity with implicit layers

We are interested in learning elastoplasticity directly from stress–strain data. Data-driven learning of plasticity is a notoriously difficult task owing to the non-smooth transition induced by the yield criterion and due to the potentially complex shape of plastic yield surfaces in a multi-dimensional space. To circumvent these issues, we present a simple machine learning architecture based on implicit layers. Such layers formulate the elastoplastic constitutive update as a convex optimization problem with learnable parameters. Parametrized classes of convex sets are proposed to describe generic plastic yield surfaces, including polyhedra, ellipsoids or spectrahedra. Examples, ranging from simple 2D domains to complex 6D shell yield surfaces demonstrate the efficiency of this implicit learning strategy. Excellent generalization is observed thanks to the embedded convex mathematical structure while requiring a low amount of learning parameters. Good performance in the low data regime and in presence of noise is also observed.