Smoothed finite element method for stress intensity factor estimation: benefits and limitations

TL;DR

This study evaluates the efficiency of smoothed finite element methods in calculating stress intensity factors for linear fracture mechanics problems, highlighting accuracy, mesh influence, and limitations like unphysical oscillations.

Contribution

It compares three smoothed FEM variants for SIF estimation, identifying $eta$-FEM as most accurate and discussing their benefits and limitations in simple benchmark problems.

Findings

$eta$-FEM shows highest accuracy among tested methods.

ES-FEM accuracy matches traditional FEM with quadratic elements.

NS-FEM overestimates SIF and causes unphysical oscillations.

Abstract

The aim of this study was to check how efficient can be smoothed finite element method (FEM) for solution of the linear fracture mechanics problems. Accuracy of stress intensity factor (SIF) computation were investigated using three types of smoothed FEM (namely ES-FEM, NS-FEM and $\alpha$-FEM). Two types of simple benchmark problems (uniaxial tension of the specimens with central and edge cracks) have been considered. SIF values were calculated by virtual crack extension and modified crack closure integral methods on almost uniform meshes. Influence of the mesh density and type of the method used for SIF determination were investigated too. Conclusions: 1) $\alpha$-FEM has the highest accuracy among all tested methods. 2) In the case of the simplest linear triangles, ES-FEM accuracy is same as in the case of traditional FEM when second order (quadratic) elements are used. 3) NS-FEM always overestimates SIF values. Unfortunately, solutions obtained using this method or $\alpha$-FEM contain unphysical oscillations of displacements and stress near the crack tip.