An eXtended Finite Element Method Implementation in COMSOL Multiphysics: Solid Mechanics

TL;DR

This paper introduces the first implementation of the eXtended Finite Element Method (XFEM) within COMSOL Multiphysics, enabling advanced crack analysis and propagation simulation with high accuracy in 2D and 3D settings.

Contribution

It develops a novel integration strategy for XFEM in COMSOL, including enrichment, crack analysis, and propagation, validated through numerical examples.

Findings

Excellent agreement with analytical, numerical, and experimental results.

Robustness demonstrated for stationary and propagating cracks in 2D and 3D.

Effective coupling of COMSOL with MATLAB for crack analysis workflows.

Abstract

This paper presents the first time implementation of the eXtended Finite Element Method (XFEM) in the general purpose commercial software COMSOL Multiphysics. An enrichment strategy is proposed, consistent with the structure of the software. To this end, for each set of enrichment functions, an additional Solid Mechanics module is incorporated into the numerical framework, coupled with compatible modifications to the internal variables. The Linear Elastic Fracture Mechanics (LEFM) is exclusively adopted for the crack analysis. The model pre-processing, level set update, stress intensity factor calculation and crack propagation analysis are conducted by employing COMSOL's built-in features in conjunction with external MATLAB functions through COMSOL LiveLink. All implementational aspects and suggested remedies for the treatment of enriched elements, framework setup, evaluation of stress intensity factors, and numerical integration are described in detail. The accuracy and robustness of the proposed method are examined by several numerical examples for stationary and propagating crack problems in 2D and 3D settings. The results represent excellent agreement with available analytical, numerical and experimental observations in the literature. Keywords:XFEM; COMSOL Multiphysics; Crack analysis; Fracture propagation