A hybrid s-version isogeometric strategy for dynamic crack propagation in 2D and 3D problems

2026-08-06

AI Summary

This study addresses the limitations in accuracy and efficiency associated with computing near-crack fracture quantities—such as dynamic stress intensity factors (DSIFs) and local stress fields—in dynamic crack propagation problems. To overcome these challenges, the authors propose a hybrid s-version isogeometric analysis method (hS-IGA), which employs B-spline basis functions over the global domain while retaining Lagrangian meshes in the crack-tip region. This approach effectively eliminates the accuracy loss typically caused by discontinuous coupling integrals between global and local domains in conventional s-methods. Notably, the proposed strategy avoids recursive mesh refinement and remains compatible with standard Gaussian quadrature, substantially enhancing computational efficiency. Numerical experiments in both two and three dimensions demonstrate that the method reduces the number of coupling integration points by approximately 81% and 95.6%, respectively, while accurately capturing DSIFs and local stress fields, thereby confirming its high efficiency and reliability.

Abstract

A hybrid s-version of isogeometric analysis (hS-IGA) strategy is proposed for accurate and efficient evaluation of near-crack fracture quantities in dynamic crack propagation analysis. The strategy retains the global-local superposition framework of the conventional s-method, while introducing B-spline basis functions only into the global discretisation and preserving a Lagrange-based local mesh in the crack domain. This hybrid formulation is motivated by the continuity-related bottleneck in the global-local coupling integration of the conventional Lagrange-based s-method, and by the need to retain a Lagrange-based local mesh for crack representation and post-processing of the dynamic stress intensity factor (DSIF) and local stress. The resulting formulation removes discontinuities in the coupling integrands caused by the global approximation and enables accurate coupling integration by standard Gauss quadrature without recursive subdivision. The proposed strategy is verified using two-dimensional stationary and dynamic straight-crack problems against the standard finite element method and the conventional s-method, and is further assessed using three-dimensional stationary and dynamically propagating circular-crack problems against the conventional s-method. Results show that the proposed hS-IGA strategy accurately evaluates the DSIF and local stress while retaining the global-local modelling advantages of the s-method. It also substantially reduces the number of integration points required for coupling integration, by approximately 81% in the two-dimensional dynamic benchmark and 95.6% in the three-dimensional dynamic benchmark relative to the conventional s-method. These results demonstrate that the proposed hS-IGA framework provides an accurate and efficient global-local strategy for dynamic crack propagation analyses requiring reliable evaluation of near-crack fracture quantities.

Problem

• dynamic crack propagation
• stress intensity factor
• global-local coupling
• isogeometric analysis
• fracture mechanics

Innovation

• hybrid s-version isogeometric analysis
• dynamic crack propagation
• global-local superposition
• stress intensity factor
• efficient coupling integration