# Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies

## TL;DR

This paper presents a straightforward and efficient implementation of the phase-field model for crack propagation in COMSOL Multiphysics, validated through various 2D and 3D case studies demonstrating its effectiveness.

## Contribution

The authors develop a simple, coupled implementation of the phase-field fracture model in COMSOL, enabling effective simulation of quasi-static and dynamic cracks without complex coding.

## Key findings

- Good agreement with previous models confirms validity.
- Implementation effectively handles complex crack patterns.
- Simulation results demonstrate computational efficiency.

## Abstract

The phase-field model (PFM) represents the crack geometry in a diffusive way without introducing sharp discontinuities. This feature enables PFM to effectively model crack propagation compared with numerical methods based on discrete crack model, especially for complex crack patterns. Due to the involvement of \phased field", phase-field method can be essentially treated a multifield problem even for pure mechanical problem. Therefore, it is supposed that the implementation of PFM based on a software developer that especially supports the solution of multifield problems should be more effective, simpler and more efficient than PFM implemented on a general finite element software. In this work, the authors aim to devise a simple and efficient implementation of phase-field model for the modelling of quasi-static and dynamic fracture in the general purpose commercial software developer, COMSOL Multiphysics. Notably only the tensile stress induced crack is accounted for crack evolution by using the decomposition of elastic strain energy. The width of the diffusive crack is controlled by a length-scale parameter. Equations that govern body motion and phase-field evolution are written into different modules in COMSOL, which are then coupled to a whole system to be solved. A staggered scheme is adopted to solve the coupled system and each module is solved sequentially during one time step. A number of 2D and 3D examples are tested to investigate the performance of the present implementation. Our simulations show good agreement with previous works, indicating the feasibility and validity of the COMSOL implementation of PFM.