Cracking elements method with 6-node triangular element

• Published in: Finite elements in analysis and design Vol. 177; p. 103421
• Main Authors: Mu, Linlong, Zhang, Yiming
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.09.2020; Elsevier BV
• Subjects: Crack opening model; Crack tips; Cracking (fracturing); Cracking elements method; Element type; Finite element method; Interpolation; Locking; Nodes; Quadrilaterals; Quasi-brittle fracture; Robustness (mathematics); Quasi-brittle fracture; Cracking elements method; Crack opening model; Element type
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2020.103421

The cracking elements method (CEM) is a novel Galerkin-based numerical approach for simulating cracking and fracturing processes. It is a crack-opening approach that avoids precise descriptions of the mechanical states of crack tips and captures the initiations and propagations of multiple cracks without nodal enrichment or crack tracking. The CEM requires element types with nonlinear interpolation of the displacement field to avoid stress-locking. In the 2D condition, the 6-node triangular element (T6) and 8-node quadrilateral element (Q8) are potential candidates. However, despite the success of the formerly proposed CEM with Q8, the CEM with T6 showed considerable mesh dependencies. In this work, to solve this problem, the CEM with T6 is further investigated. The mesh dependencies are shown to be eliminated with simple modification to the real characteristic length of the T6 element in the CEM framework. Several numerical examples with regular and irregular Q8 and T6 mixed meshes are provided, indicating the effectiveness and robustness of this approach. •The cracking elements method with 6-node triangular element (CEM-T6) is proposed in the form of vector and matrix.•For solving the mesh dependency problem of CEM-T6, a new method is proposed for determining the real value of the characteristic length of CEM-T6.•Numerical examples with irregular mixed quadrilateral and triangular meshes are investigated, indicating the robustness.