A barrier method for frictional contact on embedded interfaces

TL;DR

This paper introduces a novel barrier method for frictional contact on embedded interfaces in finite element analysis, offering robustness, accuracy control, and computational efficiency without additional degrees of freedom.

Contribution

The paper develops a barrier method that avoids inter-penetration and ill-conditioned systems, embedding interfaces within elements and eliminating the need for parameter tuning.

Findings

Method is robust for complex frictional contact problems.

Achieves contact pressure without inter-penetration.

Requires low computational cost similar to penalty methods.

Abstract

We present a barrier method for treating frictional contact on interfaces embedded in finite elements. The barrier treatment has several attractive features, including: (i) it does not introduce any additional degrees of freedom or iterative steps, (ii) it is free of inter-penetration, (iii) it avoids an ill-conditioned matrix system, and (iv) it allows one to control the solution accuracy directly. We derive the contact pressure from a smooth barrier energy function that is designed to satisfy the non-penetration constraint. Likewise, we make use of a smoothed friction law in which the stick-slip transition is described by a continuous function of the slip displacement. We discretize the formulation using the extended finite element method to embed interfaces inside elements, and devise an averaged surface integration scheme that effectively provides stable solutions without traction oscillations. Subsequently, we develop a way to tailor the parameters of the barrier method to embedded interfaces, such that the method can be used without parameter tuning. We verify and investigate the proposed method through numerical examples with varied levels of complexity. The numerical results demonstrate that the proposed method is remarkably robust for challenging frictional contact problems, while requiring low cost comparable to that of the penalty method.