A barrier method for frictional contact on embedded interfaces

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.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

We propose a barrier method for treating frictional contact on interfaces embedded in finite elements. The method has attractive features such as not introducing additional degrees of freedom or iterative steps, avoiding inter-penetration, avoiding an ill-conditioned matrix system, and direct control of solution accuracy. The method involves deriving contact pressure from a smooth barrier energy function and using a smoothed friction law. We use the extended finite element method for discretization and devise an integration scheme to provide stable solutions. The method can be tailored to embedded interfaces without parameter tuning and is highly robust and cost-effective for challenging frictional contact problems.