Deformation gradient averaging regularization for third medium contact

TL;DR

This paper introduces a novel deformation gradient averaging regularization technique for third medium contact in finite strain problems, enabling simpler implementation with first-order finite elements and improved robustness in contact simulations.

Contribution

It proposes an element-wise deformation gradient averaging regularization method that avoids additional degrees of freedom, enhancing third medium contact modeling in finite strain contexts.

Findings

Effective penalization of deformation gradient variations.

Compatibility with first-order finite element formulations.

Robust performance demonstrated on benchmark problems.

Abstract

The third medium contact method has recently come into popularity as an alternative to traditional contact methods in contexts where search for contact boundaries is problematic, i.e. topology optimization. To enforce the contact constraints, it relies on a fictitious compliant material occupying the void space. In finite strain setting, this necessitates regularization techniques to improve the behavior of the third medium material. A number of existing models rely on penalization of locally computed second gradients of displacements, either through direct calculation on second-order elements or through additional degrees of freedom. Here we propose an alternative approach using element-wise deformation gradient averaging to effectively penalize spatial variations of the deformation gradient, together with a linear elastic term enforcing constant third medium stiffness. Our approach enables the use of first-order finite element formulations without any additional degrees of freedom and is therefore easy to implement. We demonstrate the robustness of the proposed method on several well-established benchmarks.