Midplane based 3D single pass unbiased segment-to-segment contact interaction using penalty method

• A midplane-based high-accuracy unbiased contact methodology is proposed for fair treatment of surfaces without labelling them as master and slave. • The proposed methodology evaluates contact traction unbiasedly in a single pass instead of the dual-pass approach typically used to offset biasing in the master-slave treatment of surfaces. • The work also explains the different possible geometrical configurations that contacting segments can have for the evaluation of contact forces using the penalty method for nonconformal meshes. • The unbiased nature of the proposed methodology is also of direct benefit to the problems involving self-contact and large deformation. This work introduces a contact interaction methodology for an unbiased treatment of contacting surfaces without assigning surfaces as master and slave. Contact tractions between interacting discrete segments are evaluated with respect to a midplane in a single pass, inherently maintaining traction equilibrium. These tractions are based on the penalisation of true interpenetration between opposite surfaces, and the procedure of their integral for discrete contacting segments is described. A detailed examination of the possible geometric configurations of interacting 3D segments is provided to support visual understanding and better traction evaluation accuracy. The accuracy and robustness of the proposed method are validated against the analytical solutions of the contact patch test and Hertzian contact, demonstrating the capability to reproduce contact between flat and curved surfaces. The method passes the contact patch test with the uniform transmission of contact pressure matching the accuracy levels of finite elements. It converges towards the analytical solution with appropriate mesh refinement and a suitably high penalty factor in Hertzian contact. Dynamic problems involving elastic and inelastic collisions between two bars, as well as oblique collisions of cylinders, are also presented. The ability of the algorithm to resolve contacts between flat and curved surfaces in nonconformal meshes for both static and dynamic cases with high accuracy demonstrates its versatility for general contact problems, including self-contact.