# A phase-field method for modeling cracks with frictional contact

## TL;DR

This paper presents a novel phase-field method for modeling cracks with frictional contact that simplifies the representation of complex crack geometries and contact constraints without explicit algorithms.

## Contribution

It introduces a new phase-field approach that captures arbitrary crack geometries and contact conditions without requiring explicit contact algorithms.

## Key findings

- Successfully models crack growth with frictional contact.
- Verifies the method against existing discrete models.
- Demonstrates capability for complex crack and contact scenarios.

## Abstract

We introduce a phase-field method for continuous modeling of cracks with frictional contacts. Compared with standard discrete methods for frictional contacts, the phase-field method has two attractive features: (1) it can represent arbitrary crack geometry without an explicit function or basis enrichment, and (2) it does not require an algorithm for imposing contact constraints. The first feature, which is common in phase-field models of fracture, is attained by regularizing a sharp interface geometry using a surface density functional. The second feature, which is a unique advantage for contact problems, is achieved by a new approach that calculates the stress tensor in the regularized interface region depending on the contact condition of the interface. Particularly, under a slip condition, this approach updates stress components in the slip direction using a standard contact constitutive law, while making other stress components compatible with stress in the bulk region to ensure non-penetrating deformation in other directions. We verify the proposed phase-field method using stationary interface problems simulated by discrete methods in the literature. Subsequently, by allowing the phase field to evolve according to brittle fracture theory, we demonstrate the proposed method's capability for modeling crack growth with frictional contact.