  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.
