A data driven framework for evolutionary problems in solid mechanics

Abstract

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 modelling 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 presenta first analysis of the scheme regarding existence and data convergence. Encouraging numerical tests are also included.