A custom arc‐length Finite Element solver for large deformation adhesive contacts using a k‐d tree accelerated volumetric interaction scheme

Abstract

This paper introduces a Finite Element framework for large deformation adhesive contact between elastic bodies based on volume‐to‐volume interaction. A key component of this framework is a novel, customized arc‐length algorithm designed to follow the solution path through multiple snap‐through and snap‐back instabilities. Another new component is a k‐d tree based algorithm which significantly accelerates the computationally expensive volume‐to‐volume interaction calculations. This optimized Finite Element framework is then used to solve two‐body and three‐body elastic adhesive contact problems with realistic material and interaction parameters, using a 6‐12 Lennard‐Jones interaction potential. The improved efficiency of the k‐d tree based scheme makes it indispensable for interaction calculations. This paper also shows the importance of implementing adhesion‐specific customizations in the arc‐length solver.