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Kerem Ciftci, Klaus Hackl

• Data-driven computational mechanics replaces phenomenological constitutive functions by performing numerical simulations based on data sets of representative samples in stress-strain space. The distance of modeling values, e.g. stresses and strains in Gauss-points of a finite element calculation, from the data set is minimized with respect to an appropriate metric, subject to equilibrium and compatibility constraints, see [1]. Although this method operates well for non-linear elastic problems, there are challenges dealing with history-dependent materials, since one point in stress-strain space might correspond to different material behaviour. In [2], this issue is treated by including local histories into the data set. However, there is still the necessity to include models for the evolution of internal variables. Thus, a mixed formulation is obtained consisting of a combination of classical and data-driven modeling. In the presented approach, the data set is augmented with directions in the tangent space of points in stress-strain space. Moreover, the data set is classified into subsets corresponding to different material behaviour, e.g. elastic and inelastic. Based on the classification, transition rules map the modeling points to the various subsets. The approach and its performance will be demonstrated by applying it to a model of small strain elasto-plasticity with isotropic hardening.