  Model-free data-driven computational mechanics replaces phenomenological
constitutive functions by numerical simulations based on data sets of
representative samples in stress-strain space. The distance of strain and
stress pairs from the data set is minimized, subject to equilibrium and
compatibility constraints. 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 behaviour.In recent literature, this issue has been
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 of classical and data-driven modeling is
obtained. 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 behaviour. Based on
this classification, transition rules map the modeling points to the various
subsets. The approach will be applied to non-linear elasticity and
elasto-plasticity with isotropic hardening.
