A finite element formulation of non-smooth contact based on oriented volumes for quadrilateral and hexahedral elements

This paper concerns the finite element modeling of contact between solid bodies, with a special emphasis on the treatment of non-smooth conditions. A new approach for the formulation of the contact constraint that allows for a simple and unified treatment of all potential contact scenarios in the presence of large deformations is presented. Based on the calculation of an oriented volume, this approach possesses the ability to resolve complicated contact scenarios efficiently, while being simple to implement and more widely applicable than the contact formulations available to-date. We show that the formulation boils down to a node-to-surface gap function that works effectively for non-smooth contact situations. The numerical implementation using the midpoint rule shows the need to guarantee the conservation of the total energy during impact, for which a Lagrange multiplier method is used. The result is a robust contact detection and resolution algorithm.