X-IGA Used for Orthotropic Material Crack Growth

Area of Science:

• Computational mechanics
• Materials science
• Fracture mechanics

Background:

• Composite materials are susceptible to crack propagation, impacting structural integrity.
• Accurate simulation of crack growth is crucial for predicting material failure.
• Existing methods like the extended finite element method (X-FEM) show promise but can be computationally intensive.

Purpose of the Study:

• To introduce and validate a new numerical approach, extended isogeometric analysis (X-IGA), for simulating crack growth in unidirectional composites.
• To evaluate the accuracy of X-IGA in determining stress intensity factors and T-stress.
• To compare the performance of X-IGA with the extended finite element method (X-FEM).

Main Methods:

• Formulation of governing equations using energy integral method, Stroh's Formula, and anisotropic elasticity.
• Numerical solution and post-processing of stress and stress intensity factor (SIF) using developed MATLAB code.
• Validation against a benchmark problem: an anisotropic plate with two edge cracks.

Main Results:

• The proposed extended isogeometric analysis (X-IGA) effectively simulates crack growth in composite materials.
• Calculated stress intensity factors (SIF) from X-IGA show excellent agreement with X-FEM results.
• A minimal discrepancy of 0.0021 Pa·m^0.5 was observed when comparing X-IGA and X-FEM SIF values.

Conclusions:

• Extended isogeometric analysis (X-IGA) is a credible and accurate method for numerically simulating crack growth in unidirectional composites.
• The high accuracy of X-IGA suggests its potential as a robust alternative to X-FEM for analyzing composite material failure.
• This approach can enhance the design and safety of composite structures across various industries.