Curved node-to-face contact schemes for higher-order finite elements in lumped-mass explicit methods

Abstract

Contact is crucial in many lumped-mass explicit analyses, such as for high-rate impact, and enforcement methods for higher-order elements are generally less mature than for first-order ones. In this paper, basic lumped-mass explicit capabilities are pursued for three-dimensional contact/impact that account for arbitrary-order elemental curvature but with reasonable computational costs. Deformable-to-rigid and deformable-to-deformable surface-to-surface contact are considered with both triangular and/or quadrilateral faces for large deformation/sliding. Double-pass node-to-face contact searching and enforcement approaches are presented for general three-dimensional C0 higher-order Lagrange type elements in nonlinear solid dynamics using typical lumped-mass central difference time integration. This study uses classical kinematically compliant and penalty methods as well as presents modified versions better suited for higher-order Lagrange type elements. It also presents a general outer-loop iterative framework for increased accuracy and examines the simplifying practice of partitioning (subdivision) of higher-order element faces into first-order ones. Assessments are made with benchmark and practical high-rate impact applications involving elastic, hyperelastic, and elastic–plastic material models. Although subdivision into bilinear elements can sometimes be effective, it is demonstrated that they can also fail and that more precise treatment of even only modest amounts of curvature can be more reliable and improve performance.