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

Abstract

This work introduces a contact interaction methodology for an unbiased treatment of contacting surfaces without assigning surfaces as master and slave. The contact tractions between interacting discrete segments are evaluated with respect to a midplane in a single pass, inherently maintaining the equilibrium of tractions. 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 in this paper. A meticulous examination of the different possible geometric configurations of interacting 3D segments is presented to develop 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, two-beam bending, Hertzian contact, and flat punch test, thus proving the capability to reproduce contact between flat surfaces, curved surfaces, and sharp corners in contact, respectively. 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 mesh refinement and a suitably high penalty factor. The effectiveness of the proposed algorithm also extends to self-contact problems and has been tested for self-contact between flat and curved surfaces with inelastic material. Dynamic problems of elastic and inelastic collisions between bars, as well as oblique collisions of cylinders, are also presented. The ability of the algorithm to resolve contacts between flat and curved surfaces for nonconformal meshes with high accuracy demonstrates its versatility in general contact problems.