A dual-free reduced-order modeling strategy for parametrized variational inequalities with application to contact mechanics

We propose a novel reduced-order modeling approach for parametrized variational inequalities applied to contact mechanics. Traditional reduced-basis methods for variational inequalities rely on mixed primal-dual formulations, which face difficulties in dual reduction, due to the requirement to preserve the non-negativity of dual variables. To address these challenges, we propose an exclusively primal formulation that circumvents dual cone compression. The resulting reduced model guarantees feasibility with respect to inequality constraints and offers substantial computational savings without compromising accuracy. The proposed reduction strategy is applied to elastic frictionless contact mechanics under small deformations with matching meshes. Numerical experiments are presented to demonstrate the robustness and efficiency of the proposed method.