A novel X-FEM based fast computational method for crack propagation

TL;DR

This paper introduces a fast, efficient computational method based on X-FEM for simulating crack propagation, significantly reducing computational effort by local updating of the stiffness matrix.

Contribution

It proposes the decomposed updating reanalysis (DUR) method, a novel local updating strategy for X-FEM that enhances efficiency without sacrificing accuracy.

Findings

DUR method reduces computational time significantly.

High accuracy maintained in crack propagation simulations.

Validated through multiple numerical examples.

Abstract

This study suggests a fast computational method for crack propagation, which is based on the extended finite element method (X-FEM). It is well known that the X-FEM might be the most popular numerical method for crack propagation. However, with the increase of complexity of the given problem, the size of FE model and the number of iterative steps are increased correspondingly. To improve the efficiency of X-FEM, an efficient computational method termed decomposed updating reanalysis (DUR) method is suggested. For most of X-FEM simulation procedures, the change of each iterative step is small and it will only lead a local change of stiffness matrix. Therefore, the DUR method is proposed to predict the modified response by only calculating the changed part of equilibrium equations. Compared with other fast computational methods, the distinctive characteristic of the proposed method is to update the modified stiffness matrix with a local updating strategy, which only the changed part of stiffness matrix needs to be updated. To verify the performance of the DUR method, several typical numerical examples have been analyzed and the results demonstrate that this method is a highly efficient method with high accuracy.