A computational contact formulation based on surface potentials

This work presents the theory and numerical implementation of a contact formulation based on surface potentials. The new theory formulates contact based on distance-dependent surface interaction potentials and distinguishes between three interaction classes: point interaction, short-range surface interaction and long-range surface interaction. Here the focus is placed on frictionless contact, although the first class readily admits frictional sticking contact as is also shown. The proposed contact theory provides a unified framework for various contact formulations, ranging from numerical constraint formulations, like penalty, barrier, cross-constrained and augmented Lagrange multiplier methods, to physical interaction formulations, like cohesive zone models, as well as electrostatic, gravitational and van-der-Waals interaction. Apart from recovering classical penalty and barrier formulations, the new theory also naturally leads to a modified penalty and barrier method. The formulation also recovers classical one-pass contact algorithms, however the real advantages lie in a novel two-pass contact algorithm, denoted the two-half-pass contact algorithm, since each pass only accounts for the contact forces acting on the slave body. This implies that traction continuity is only satisfied in theory, but not imposed a priori in the algorithm. Instead, it is obtained naturally to high accuracy as is demonstrated by several 2D and 3D numerical examples. These include sliding contact, peeling contact and electrostatic attraction between deformable solids. Among the examples is a detailed comparison between the new formulation and classical one-pass approaches. It is further shown that the new contact formulation passes the contact patch test.