# X-IGA Used for Orthotropic Material Crack Growth

## TL;DR

The paper introduces X-IGA, a new numerical method for simulating crack growth in composite materials, validated against existing methods with high accuracy.

## Contribution

The novel contribution is the development and validation of extended isogeometric analysis (X-IGA) for crack growth simulation in anisotropic materials.

## Key findings

- The X-IGA results for stress intensity factors closely match those from X-FEM with a discrepancy of 0.0021 Pa·m0.5.
- The method is validated using an anisotropic plate with edge cracks, showing strong agreement with established techniques.

## Abstract

In this paper, we propose a new approach for numerically simulating the growth of cracks in unidirectional composite materials, termed extended isogeometric analysis, evaluating the maximum stress intensity factor and T-stress. To validate our approach, we used a small anisotropic plate with two edge cracks, beginning with formulating the governing equations based on the energy integral method, Stroh’s Formula, and the Elastic Law describing the behaviour of anisotropic materials, while considering boundary conditions and initial states. A MATLAB code was developed to solve these equations numerically and to post-process the tensile stress and the stress intensity factor (SIF) in the first mode. The results for the SIF closely match those obtained using the extended finite element method (X-FEM), with a discrepancy of only 0.0021 Pa·m0.5. This finding underscores the credibility of our approach. The extended finite element method has demonstrated robustness in predicting crack propagation in composite materials in recent years, leading to its adoption by several widely used software packages in various industries.