A three-dimensional surface stress tensor formulation for simulation of adhesive contact in finite deformation

A three-dimensional surface adhesive contact formulation is proposed to simulate macroscale adhesive contact interaction characterized by the van der Waals interaction between arbitrarily shaped deformable continua under finite deformation. The proposed adhesive contact formulation uses a double-layer surface integral to replace the conventional double volume integration to compute the adhesive contact force vector. Considering nonlinear finite deformation, we have derived the surface stress tensor and the corresponding tangent stiffness matrix in a Galerkin weak formulation. With the surface stress formulation, the adhesive contact problems are solved in the framework of nonlinear continuum mechanics by using the standard Lagrange finite element method. Surface stress tensors are formulated for both interacting bodies. Numerical examples show that the proposed surface contact algorithm is accurate, efficient, and reliable for three-dimensional adhesive contact problems of large deformations for both quasi-static and dynamic simulations. Copyright (c) 2015 John Wiley & Sons, Ltd.