Patch based unbiased 3D frictional contact formulation for finite element algorithms

Abstract

A new truly unbiased frictional contact formulation exclusively leveraging the midplane-based segment-to-segment (STS) interaction with a predictor–corrector approach is presented. Unlike the traditional master–slave based dual pass approaches, this formulation only requires a single pass providing a computational advantage in comparison. This work details the development of a penalty-regularised frictional contact between discretised surfaces following an equivalent description in the continuum space. The relative motion between the contacting segments is studied through changes in the interacting convective coordinates in overlapping regions, thus ensuring an unbiased formulation without labelling surfaces as master and slave. Here, the stick–slip frictional states are enforced over interacting regions (patches) of all STS pairs instead of the node on segment pairs by utilising the return mapping algorithm. The formulation inherently maintains the traction equality on opposite surfaces of all contact pairs. The robustness of the formulation is demonstrated through several examples with varying contact conditions of stick–slip states and transition in static and dynamic problems including flat and curved surfaces, rolling effect, self-contact and impact.