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In a wide range of practical problems, such as forming operations and impacttests, assuming that one of the contacting bodies is rigid is an excellentapproximation to the physical phenomenon. In this work, the well-establisheddual mortar method is adopted to enforce interface constraints in the finitedeformation frictionless contact of rigid and deformable bodies. The efficiencyof the nonlinear contact algorithm proposed here is based on two maincontributions. Firstly, a variational formulation of the method using theso-called Petrov-Galerkin scheme is investigated, as it unlocks a significantsimplification by removing the need to explicitly evaluate the dual basisfunctions. The corresponding first-order dual mortar interpolation is presentedin detail. Particular focus is, then, placed on the extension for second-orderinterpolation by employing a piecewise linear interpolation scheme, whichcritically retains the geometrical information of the finite element mesh.Secondly, a new definition for the nodal orthonormal moving frame attached toeach contact node is suggested. It reduces the geometrical coupling between thenodes and consequently decreases the stiffness matrix bandwidth. The proposedcontributions decrease the computational complexity of dual mortar methods forrigid/deformable interaction, especially in the three-dimensional setting,while preserving accuracy and robustness.

An Efficient Contact Algorithm for Rigid/Deformable Interaction based on the Dual Mortar Method