A corotational hybrid-Trefftz stress formulation for modelling cohesive cracks

• Published in: Computer methods in applied mechanics and engineering 2009-03, Vol.198 (15), p.1298-1310
• Main Authors: Kaczmarczyk, Łukasz, Pearce, Chris J.
• Format: Article
• Language: English
• Subjects: Cohesive crack; Computational techniques; Corotational formulation; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fracturing; Fundamental areas of phenomenology (including applications); Hybrid-Trefftz elements; Mathematical methods in physics; Physics; Solid mechanics; Structural and continuum mechanics
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2008.11.018

This paper presents a corotational hybrid-Trefftz formulation for modelling propagating cohesive cracks and captures moderate rotations but small strains. The formulation is characterised by the fact that stresses are approximated within the domain of the element and the stiffness can be expressed via a boundary rather than a domain integral. Thus, compared to their FEM counterpart, hybrid-Trefftz stress elements exhibit faster convergence of the stress fields. Furthermore, the displacements are approximated on element boundaries and the displacement basis is defined independently on each element interface. Thus, the overall bandwidth of the stiffness matrix is very small and computationally efficient to solve. A corotational formulation for hybrid-Trefftz elements is also introduced in order to capture the effect of geometric nonlinearities in the form of moderate rotations. The model’s performance is demonstrated on three examples, illustrating crack propagation and the influence of geometric nonlinearities.