A data-driven framework for evolutionary problems in solid mechanics

Data-driven schemes introduced a new perspective in elasticity: While certain physical principles are regarded as invariable, material models for the relation between strain and stress are replaced by data clouds of admissible pairs of these variables. A data-driven approach is of particular interest for plasticity problems, since the material modeling is even more unclear in this field. Unfortunately, so far, data-driven approaches to evolutionary problems are much less understood. We try to contribute in this area and propose an evolutionary data-driven scheme. We present a first analysis of the scheme regarding existence and data convergence. Encouraging numerical tests are also included.