Data-Driven simulation of inelastic materials using structured data sets, tangent space information and transition rules

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 integration 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 Kirchdoerfer et al. 2016, Kirchdoerfer et al. 2017, Conti et al. 2018. Although this method operates well for non-linear elastic problems, there are challenges dealing with history-dependent materials, since one and the same point in stress-strain space might correspond to different material behavior. In Eggersmann et al. 2019, 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 specific 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 divided into subsets corresponding to different material behavior, e.g. elastic and inelastic. Based on the classification, transition rules map the modeling points to the various subsets. The approach and its numerical performance will be demonstrated by applying it to models of non-linear elasticity and elasto-plasticity with isotropic hardening.