  In this work we consider the hybrid Data-Driven Computational Mechanics
(DDCM) approach, in which a smooth constitutive manifold is reconstructed to
obtain a well-behaved nonlinear optimization problem (NLP) rather than the much
harder discrete-continous NLP (DCNLP) of the direct DDCM approach. The key
focus is on the addition of geometric inequality constraints to the hybrid DDCM
formulation. Therein, the required constraint force leads to a contact problem
in the form of a mathematical program with complementarity constraints (MPCC),
a problem class that is still less complex than the DCNLP. For this MPCC we
propose a heuristic quick-shot solution approach, which can produce verifiable
solutions by solving up to four NLPs. We perform various numerical experiments
on three different contact problems of increasing difficulty to demonstrate the
potential and limitations of this approach.
