A data-driven reduced-order surrogate model for entire elastoplastic simulations applied to representative volume elements

This contribution discusses surrogate models that emulate the solution field(s) in the entire simulation domain. The surrogate uses the most characteristic modes of the solution field(s), in combination with neural networks to emulate the coefficients of each mode. This type of surrogate is well known to rapidly emulate flow simulations, but rather new for simulations of elastoplastic solids. The surrogate avoids the iterative process of constructing and solving the linearized governing equations of rate-independent elastoplasticity, as necessary for direct numerical simulations or (hyper-)reduced-order-models. Instead, the new plastic variables are computed only once per increment, resulting in substantial time savings. The surrogate uses a recurrent neural network to treat the path dependency of rate-independent elastoplasticity within the neural network itself. Because only a few of these surrogates have been developed for elastoplastic simulations, their potential and limitations are not yet well studied. The aim of this contribution is to shed more light on their numerical capabilities in the context of elastoplasticity. Although more widely applicable, the investigation focuses on a representative volume element, because these surrogates have the ability to both emulate the macroscale stress-deformation relation (which drives the multiscale simulation), as well as to recover all microstructural quantities within each representative volume element.