Computational science

Algorithm

Engineering

Philosophy

Stress field

Stress intensity factor

Statistics

Materials science

Singularity

Adaptive mesh refinement

Discontinuity (linguistics)

Computer science

A priori and a posteriori

Orthotropic material

Finite element method

Mathematics

Estimator

Epistemology

Mathematical analysis

Composite material

Isogeometric analysis

Structural engineering

Fracture (geology)

Fracture mechanics

Composites Part B Engineering

This paper is concerned with the numerical investigation of fracture mechanics parameters for cracked orthotropic composite structures by using an efficient computational approach. The adaptive extended isogeometric analysis (XIGA) based on locally refined (LR) B-splines is thus developed. This adaptive XIGA is enhanced by both signed-distance and orthotropic crack-tip enrichment functions to represent strong discontinuity and singularity induced by crack, respectively. In addition, to improve the integration accuracy, the 'sub-triangle' and 'almost polar' techniques are adopted for the cut and crack tip elements, respectively. For adaptivity, the smoothed stress field is achieved to develop the posteriori error estimator based local refinement, according to the Zienkiewicz–Zhu estimation. Such posteriori error estimator is then used to determine refinement domains, where the local refinement takes place. The proposed approach is applied for fracture analyses of orthotropic composites, in which the stress intensity factors (SIFs) are evaluated using the contour interaction integral technique. The accuracy of the proposed adaptive orthotropic XIGA is validated through a comparison of SIFs obtained from the proposed method and the available reference solutions. Furthermore, numerical results show that the convergence rate of the adaptive local refinement is faster than that of the global refinement approach.

Adaptive orthotropic XIGA for fracture analysis of composites