Global cracking elements: A novel tool for Galerkin‐based approaches simulating quasi‐brittle fracture

• Published in: International journal for numerical methods in engineering Vol. 121; no. 11; pp. 2462 - 2480
• Main Authors: Zhang, Yiming, Mang, Herbert A.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 15.06.2020
• Subjects: Brittle fracture; Computer simulation; Crack initiation; Crack propagation; Crack tips; Cracking (fracturing); cracking elements method; Finite element method; finite‐element method (FEM); Galerkin method; Numerical stability; Quadrilaterals; quasi‐brittle fracture; Robustness (mathematics); self‐propagating crack; standard Galerkin form
• DOI: 10.1002/nme.6315
• ISSN: 0029-5981

Summary Following the so‐called cracking elements method (CEM), we propose a novel Galerkin‐based numerical approach for simulating quasi‐brittle fracture, named global cracking elements method (GCEM). For this purpose the formulation of the original CEM is reorganized. The new approach is embedded in the standard framework of the Galerkin‐based finite‐element method (FEM), which uses disconnected element‐wise crack openings for capturing crack initiation and propagation. The similarity between the proposed global cracking elements (GCEs) and the standard nine‐node quadrilateral element (Q9) suggests a special procedure: the degrees of freedom of the center node of the Q9, originally defining the displacements, are “borrowed” to describe the crack openings of the GCE. The proposed approach does not need remeshing, enrichment, or a crack‐tracking strategy, and it avoids a precise description of the crack tip. Several benchmark tests provide evidence that the new approach inherits from the CEM most of the advantages. The numerical stability and robustness of the GCEM are better than the ones of the CEM. However, presently only quadrilateral elements with nonlinear interpolations of the displacement field can be used.