Cracking elements method with 6-node triangular element

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 wi...

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Published inFinite elements in analysis and design Vol. 177; p. 103421
Main Authors Mu, Linlong, Zhang, Yiming
Format Journal Article
LanguageEnglish
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
Online AccessGet full text
ISSN0168-874X
1872-6925
DOI10.1016/j.finel.2020.103421

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Abstract 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.
AbstractList 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.
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.
ArticleNumber 103421
Author Zhang, Yiming
Mu, Linlong
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Keywords Quasi-brittle fracture
Cracking elements method
Crack opening model
Element type
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Snippet The cracking elements method (CEM) is a novel Galerkin-based numerical approach for simulating cracking and fracturing processes. It is a crack-opening...
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SubjectTerms Crack opening model
Crack tips
Cracking (fracturing)
Cracking elements method
Element type
Finite element method
Interpolation
Locking
Nodes
Quadrilaterals
Quasi-brittle fracture
Robustness (mathematics)
Title Cracking elements method with 6-node triangular element
URI https://dx.doi.org/10.1016/j.finel.2020.103421
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