Cracking elements method with 6-node triangular element

Mu, Linlong; Zhang, Yiming

doi:10.1016/j.finel.2020.103421

Cited by 22 publications

(17 citation statements)

References 70 publications

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“…Since the details of the CEM were proposed in [56,57] in matrix form, only a brief introduction will be provided in this section. By providing the elemental stiffness matrix and residual vector of uncracked and cracked elements, we will demonstrate the ease of implementing the CEM in the FEM framework.…”

Section: Methodsmentioning

confidence: 99%

“…Here, the determination of A (e) for the 8-node quadrilateral (Q8) and 6-node triangular (T6) elements is slightly different insofar as the equivalent crack passes through the center point of Q8 but through the midpoint of one edge of T6; see Figure 2. More details can be found in [56,57]. Its elemental stiffness matrix K (e) can be obtained as K (e) j−1 = B (e) T C (e) B (e) d(e) + 0 0 0 A (e) D (e) .…”

Section: Cracking Elementmentioning

confidence: 99%

“…The bottom 0.4 cm width of the disk is fixed when the top 0.4 cm width of the disk is vertically loaded. The elastic modulus E is 15 GPa, the Poisson's ratio ν is 0.21, the fracture energy G f is 30 N/m, and the tensile strength f t is 3.81 MPa, see the model provided in [57]. The analytical peak load per unit thickness is F peak = (π D f t )/2 = 598.47 kN, which is used for obtaining the normalized peak loads.…”

Section: Disk Testsmentioning

confidence: 99%

“…Finally, we hope that multiple cracks can be efficiently tracked simultaneously and that complicated crack tracking strategies [52,53] can be avoided. The cracking elements method (CEM) [54][55][56][57] is the chosen numerical tool.…”

Section: Introductionmentioning

confidence: 99%

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Applying the Cracking Elements Method for Analyzing the Damaging Processes of Structures with Fissures

Dong

Sun

et al. 2020

Applied Sciences

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In this work, the recently proposed cracking elements method (CEM) is used to simulate the damage processes of structures with initial imperfections. The CEM is built within the framework of the conventional finite element method (FEM) and is formally similar to a special type of finite element. Disconnected piecewise cracks are used to represent the crack paths. With the advantage of the CEM for which both the initiation and propagation of cracks can be captured naturally, we numerically study uniaxial compression tests on specimens with multiple joints and fissures, where the cracks may propagate from the tips or from other unexpected positions. Although uniaxial compression tests are considered, tensile damage criteria are mainly used in the numerical model. On the one hand, the results demonstrate the robustness and effectiveness of the CEM, while, on the other hand, some drawbacks of the present model are demonstrated, indicating directions for future work.

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Section: Methodsmentioning

confidence: 99%

Section: Cracking Elementmentioning

confidence: 99%

Section: Disk Testsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Applying the Cracking Elements Method for Analyzing the Damaging Processes of Structures with Fissures

Dong

Sun

et al. 2020

Applied Sciences

Self Cite

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“…Finally, we hope multiple cracks can be efficiently and simultaneously tracked and complicated crack tracking strategies [52,53] can be avoided. The Cracking Elements Method (CEM) [54][55][56][57] is the chosen numerical tool.…”

Section: Introductionmentioning

confidence: 99%

Applying the Cracking Elements Method for Analyzing the Damaging Processes of Structures with Fissures

Dong¹,

Wu²,

Sun³

et al. 2020

Preprint

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In this work, the recently proposed cracking elements method (CEM) is used for simulating the damaging processes of structures with initial imperfections. CEM is built in the framework of conventional FEM which is formally like a special type of finite element. The disconnected piecewise cracks are used for representing crack paths. Taking the advantages of CEM that both the initiations and propagations of cracks can be naturally captured, we numerically study the uni-axial compression tests of specimens with multiple joints and fissures, where the cracks may propagate from the tips, or from some other unexpected positions. Though uni-axial compression tests are considered, mainly tensile damage criteria are used in the numerical model. On one hand, the results demonstrate the robustness and effectiveness of the CEM while on the other hand, some drawbacks of the present model are demonstrated, showing the future work.

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An XFEM multilayered heaviside enrichment for fracture propagation with reduced enhanced degrees of freedom

Bybordiani

Latifaghili

Soares

et al. 2021

Numerical Meth Engineering

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The development of advanced numerical techniques such as eXtended/ Generalized Finite Elements Methods (XFEM/GFEM) has provided means for accurate prediction of material failure. However, the present theories mostly rely on a global formulation, where the system of equations is subject to progressive dimension increase with crack evolution. In this regard, an independent multilayered enrichment is proposed for the XFEM/GFEM family of methods where a few elements in close proximity are assigned to an enrichment layer independent of the remaining ones. The enhanced degrees of freedom can be condensed out at the layer level, which leads to system dimensions, sparsity, and bandness identical to those of the underlying finite elements. Nodal and elemental enrichment methods are shown to be particular limit cases of present approach. The robustness of the proposed approach is first demonstrated in element-level examples. The use of only few adjacent elements in a group enrichment is shown to suffice for acceptable results while the order of the condition number of the final stiffness matrix resembles the underlying uncracked finite element counterpart. Finally, using several structural examples, the accuracy and robustness of the method is shown in terms of force-displacement response, stress fields, and traction continuity in nonlinear problems.

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Cracking elements method with 6-node triangular element

Cited by 22 publications

References 70 publications

Applying the Cracking Elements Method for Analyzing the Damaging Processes of Structures with Fissures

Applying the Cracking Elements Method for Analyzing the Damaging Processes of Structures with Fissures

Applying the Cracking Elements Method for Analyzing the Damaging Processes of Structures with Fissures

An XFEM multilayered heaviside enrichment for fracture propagation with reduced enhanced degrees of freedom

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