(Model-Free) Data-Driven Computational Mechanics (DDCM) method departs from classical PDE-
based formulations by replacing constitutive laws with raw material data, leading to a variational prob-
lem formulated as a double minimisation between mechanically admissible states and data-consistent
states. While many of the mechanical admissibility constraints can be enforced naturally within a finite
element setting, others require special treatment in the data-driven context. In this work, we focus on
unilateral constraints arising in contact mechanics, formulated as nonlinear complementarity conditions
of Signorini type. Such constraints have not yet been addressed within the DDCM framework, despite
their practical relevance and nontrivial treatment. We first introduce a one-dimensional prototype prob-
lem to illustrate the main ideas and numerical challenges. The proposed formulation extends DDCM to
contact problems and lays the groundwork for data-driven simulations involving inequality-constrained
mechanics.