An adaptive finite element procedure for crack propagation analysis

Alshoaibi, Abdulnaser M.; Hadi, Muhammad Salihi Abdul; Ariffin, A. K.

doi:10.1631/jzus.2007.a0228

Cited by 20 publications

(16 citation statements)

References 14 publications

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“…It is therefore important to develop a numerical model capable of calculating these factors for different geometries of cracked structures under different boundary conditions. In this paper, the displacement extrapolation method 28,29 is used to calculate the stress intensity factors K I and K II as follows: In order to obtain a better approximation of the field near the crack tip, special quarter point finite elements proposed by Barsoum 30 are used where the mid-side node of the element in the crack tip is moved to 1/4 of the length of the element L.…”

Section: Numerical Calculation Of Stress Intensity Factorsmentioning

confidence: 99%

Numerical Modelling of Crack Propagation in Cement PMMA: Comparison of Different Criteria

2016

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Modelling of a crack propagating through a finite element mesh under mixed mode conditions is of prime importance in fracture mechanics. In this paper, three different crack growth criteria and the respective crack paths prediction in the cement mantle of the reconstructed acetabulum are compared. The maximum tangential stress (MTS) criterion, the minimum strain energy density (MSED) criterion and the new general fracture criterion based on the energy release rate G(θ) are investigated using advanced finite element technique. The displacement extrapolation technique (DET) is used, to obtain the SIFs at crack tip. Several examples are presented to show the robustness of the numerical techniques. The effect of the inclusions and cavities on the crack propagation in cement orthopedic are highlighted.

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Section: Numerical Calculation Of Stress Intensity Factorsmentioning

confidence: 99%

Numerical Modelling of Crack Propagation in Cement PMMA: Comparison of Different Criteria

2016

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“…Here stress error norm is taken as the error estimator. The strategy used to refine the mesh during analysis process is adopted from Alshoaibi et al [4,5] .…”

Section: The Simulation Modelmentioning

confidence: 99%

Development of Efficient Finite Element Software of Crack Propagation Simulation using Adaptive Mesh Strategy

Alshoaibi¹

2009

American Journal of Applied Sciences

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Abstract:The purpose of this study is on the determination of 2D crack paths and surfaces as well as on the evaluation of the stress intensity factors as a part of the damage tolerant assessment. Problem statement: The evaluation of SIFs and crack tip singular stresses for arbitrary fracture structure are a challenging problem, involving the calculation of the crack path and the crack propagation rates at each step especially under mixed mode loading. Approach: This study was provided a finite element code which produces results comparable to the current available commercial software. Throughout the simulation of crack propagation an automatic adaptive mesh was carried out in the vicinity of the crack front nodes and in the elements which represent the higher stresses distribution. The finite element mesh was generated using the advancing front method. The adaptive remising process carried out based on the posteriori stress error norm scheme to obtain an optimal mesh. The onset criterion of crack propagation was based on the stress intensity factors which provide as the most important parameter that must be accurately estimated. Facilitated by the singular elements, the displacement extrapolation technique is employed to calculate the stress intensity factor. Crack direction is predicted using the maximum circumferential stress theory. The fracture was modeled by the splitting node approach and the trajectory follows the successive linear extensions of each crack increment. The propagation process is driven by Linear Elastic Fracture Mechanics (LEFM) approach with minimum user interaction. Results: In evaluating the accuracy of the estimated stress intensity factors and the crack path predictions, the results were compared with sets of experimental data, benchmark analytical solutions as well as numerical results of other researchers. Conclusion/Recommendations: The assessment indicated that the program was highly reliable to evaluate the stress intensity factors and successfully predicts the cracks trajectories. Based on the results, it was recommended to add further development in the software to simulate crack propagation in elastoplastic materials.

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“…The special hierarchic structure generated during the division of finite element edges serves to construct a sequence of very efficient preconditioners. These preconditioners are used in association with the conjugate gradient method by the solution of the systems of linear equations (37) obtained after discretizations of the variational formulation (14) in the iterative mesh modification (refinement and/or coarsening) process. The idea of the hierarchic preconditioner was introduced by Yserentant in [29] and is based on the observation that in a so-called hierarchic basis the stiffness matrix C has a good condition number.…”

Section: Hierarchic Preconditionermentioning

confidence: 99%

“…It allows to model growing cracks without mesh conforming to their portions. Consequently, contrary to the corresponding standard finite element algorithm presented, for example, in [14] by Alshoaibi et al, no remeshing of the domain after each propagation step is necessary. Additionally, the X-FEM applied to crack problems helps to capture the near-tip crack fields more efficiently than the standard one, because of the already mentioned enrichment.…”

Section: Introductionmentioning

confidence: 98%

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Adaptive finite element computation of dielectric and mechanical intensity factors in piezoelectrics with impermeable cracks

Jański

Scherzer

Steinhorst

et al. 2009

Numerical Meth Engineering

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SUMMARYThe paper deals with the application of an adaptive, hierarchic-iterative finite element technique to solve two-dimensional electromechanical boundary value problems with impermeable cracks in piezoelectric plates. In order to compute the dielectric and mechanical intensity factors, the interaction integral technique is used. The iterative finite element solver takes advantage of a sequence of solutions on hierarchic discretizations. Based on an a posteriori error estimation, the finite element mesh is locally refined or coarsened in each step. Two crack configurations are investigated in an infinite piezoelectric plate: A finite straight crack and a finite kinked crack. Fast convergence of the numerical intensity factors to the corresponding analytical solution is exemplarily proved during successive adaptive steps for the first configuration. Similar tendency can be observed for the second configuration. Furthermore, the computed intensity factors for the kinks are found to coincide well with the corresponding analytical values. In order to simulate the kinks spreading from a straight crack, the finite element mesh is modified automatically with a specially developed algorithm. This forms the basis for a fully adaptive simulation of crack propagation.

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An adaptive finite element procedure for crack propagation analysis

Cited by 20 publications

References 14 publications

Numerical Modelling of Crack Propagation in Cement PMMA: Comparison of Different Criteria

Numerical Modelling of Crack Propagation in Cement PMMA: Comparison of Different Criteria

Development of Efficient Finite Element Software of Crack Propagation Simulation using Adaptive Mesh Strategy

Adaptive finite element computation of dielectric and mechanical intensity factors in piezoelectrics with impermeable cracks

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