A Bézier-Based Numerical Approach for Static Fracture Analysis of Cracked Plates Using Peridynamics Theory

This study investigates the static analysis of cracked plates using a Bézier-based method within the framework of Peridynamics (PD) theory. The research focuses on modeling crack propagation in rectangular plates under various boundary and initial conditions, employing a novel numerical approach that integrates Bézier curves with PD theory. The proposed method addresses the limitations of traditional numerical techniques, such as the finite element method, which struggle with discontinuities like cracks. By leveraging the parametric nature of Bézier curves, the study achieves high accuracy and stability in predicting crack growth. The results are compared with those obtained from adaptive dynamic relaxation (ADR) and direct integration methods, highlighting the computational efficiency and precision of the Bézier-based approach. The findings demonstrate that the Bézier method offers superior stability and accuracy, albeit at a higher computational cost, making it a viable alternative for static analysis in fracture mechanics. The study also introduces a modified bond-based Peridynamics (MBB-PD) model, which eliminates restrictions on Poisson's ratio and incorporates novel failure criteria for normal and shear strain bonds. This model shows excellent agreement with numerical and experimental results, further validating its effectiveness. Future research could focus on optimizing the computational efficiency of the Bézier method for large-scale applications.

کلیدواژه ها:

Peridynamics ، Bezier Method ، Failure ، Damage ، Mode I