Overview
A hybrid s-version isogeometric analysis (hS-IGA) strategy has been developed for the evaluation of near-crack fracture quantities during dynamic crack propagation. This strategy aims to improve accuracy and efficiency in dynamic crack propagation analysis by retaining the global-local superposition framework of the conventional s-method while integrating B-spline basis functions into the global discretization. It maintains a Lagrange-based local mesh within the crack domain.
Research Context
The conventional s-method, which uses a global-local superposition framework, presents challenges related to continuity in the coupling integration when Lagrange-based elements are used globally. This continuity-related bottleneck can affect the accuracy of coupling integration. Additionally, the representation of cracks and post-processing of quantities like the dynamic stress intensity factor (DSIF) and local stress often necessitates a Lagrange-based local mesh.
Approach
The proposed hS-IGA strategy addresses the continuity issues in coupling integration by introducing B-spline basis functions for the global discretization. This hybrid approach specifically aims to remove discontinuities in the coupling integrands that arise from global approximation. By doing so, it facilitates accurate coupling integration using standard Gauss quadrature, eliminating the need for recursive subdivision. The strategy maintains a Lagrange-based local mesh in the crack domain for crack representation and for the post-processing of the DSIF and local stress.
Findings
The hS-IGA strategy was verified against established methods using both two-dimensional (2D) stationary and dynamic straight-crack problems, comparing its performance to the standard finite element method and the conventional s-method. Further assessment involved three-dimensional (3D) stationary and dynamically propagating circular-crack problems, comparing results against the conventional s-method.
- The hS-IGA strategy accurately evaluated the DSIF and local stress in the assessed problems.
- It maintained the global-local modeling advantages inherent to the s-method.
- The proposed strategy substantially reduced the number of integration points required for coupling integration.
- In the 2D dynamic benchmark, the reduction was approximately 81% compared to the conventional s-method.
- In the 3D dynamic benchmark, the reduction was approximately 95.6% relative to the conventional s-method.
Why This Matters
The hS-IGA framework provides an accurate and efficient global-local strategy for dynamic crack propagation analyses. Its ability to reliably evaluate near-crack fracture quantities, coupled with the substantial reduction in computational cost for coupling integration, indicates potential benefits for analyses requiring high precision in fracture mechanics.