A contact algorithm for cohesive cracks in the extended finite element method

Fang, Heng; Zhang, Dingli; Zhou, Mingchao; Fang, Qian; Wen, Ming

doi:10.1002/nme.6329

Cited by 16 publications

(9 citation statements)

References 43 publications

(55 reference statements)

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“…The geometry of internal cracks is separated from the finite element mesh, so there is no need to regenerate the mesh as the crack expands. This feature makes XFEM a powerful tool for analyzing crack propagation [32][33][34][35].…”

Section: Numerical Experiments Of the Fracture Behavior Of Tunnel Liningsmentioning

confidence: 99%

Analysis of Crack Formation and Growth in Tunnel Linings Using Double-K Fracture Criterion

Huang

Wen

2022

Applied Sciences

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Empirical criteria and fracture/damage mechanics are used to evaluate the safety of lining cracks in the conventional methods. However, the former lacks a scientific basis, and the latter requires complicated mechanical calculations. To overcome the above shortcomings, this paper proposes a new method to perform crack analysis of plain concrete linings, based on the double-K fracture criterion. The proposed method uses two crack width indices, i.e., initiation and unstable fracture widths, to divide the fracture process of lining into three stages: initiation stage, stable propagation stage, and instability propagation stage. These two crack width indices are calculated by the equivalent transformation of fracture toughness. Using the proposed criterion, the safety state of the concrete lining can be determined by comparing the field measurement width and crack width indices. A specific code based on the extended finite element method (XFEM) is developed to simulate the fracture process of concrete lining. Several numerical experiments are carried out to evaluate the proposed fracture criterion. The results show that the two fracture indices of the proposed criterion can accurately identify two demarcation points of the three stages of the lining fracture process, including the nonlinear starting point and the unstable fracture point of the load–displacement curve. Compared with conventional methods, the proposed method uses the geometric parameter to estimate the mechanical state of cracks, so the complicated mechanical calculation can be avoided.

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Section: Numerical Experiments Of the Fracture Behavior Of Tunnel Liningsmentioning

confidence: 99%

Analysis of Crack Formation and Growth in Tunnel Linings Using Double-K Fracture Criterion

Huang

Wen

2022

Applied Sciences

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“…Therefore, the particular issue of multiple-crack problems is to identify the correct crack propagation pattern. 8 This process requires to determine the cracking behavior of each crack including the extension of active cracks and the closure of inactive cracks. Moreover, the complexity of multiple-crack problems also originates from the numerical aspect, where the numerical treatment of multiple crack surfaces requires a flexible and applicable modeling technique.…”

Section: Introductionmentioning

confidence: 99%

“…Only a few cracks will propagate continuously during the whole service period, while others will later be proved inactive and not affect the structural safety. Therefore, the particular issue of multiple‐crack problems is to identify the correct crack propagation pattern 8 . This process requires to determine the cracking behavior of each crack including the extension of active cracks and the closure of inactive cracks.…”

Section: Introductionmentioning

confidence: 99%

A numerical algorithm for multiple cracks propagation in concrete structure

Wen

Fang

Zhang

et al. 2020

Structural Concrete

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Multiple cracks are extremely common in aged or partially damaged concrete structures. These cracks have a decisive influence on the safety of structures. In this study, a novel multiple-crack-length-controlled method is presented for analyzing the cracking behavior of multiple cracks in concrete structures. This method introduces topological variables into the finite element calculation to identify the correct crack propagation pattern of multiple-crack problems. The values of topological variables that are used to active and inactive cracks are continually updated by the maximum stress criterion during calculation. The mathematical formulation of the proposed method is constructed in the incremental form. Thus, it is easy to be implemented in the nonlinear problems and capable of considering the influences of stress history on the plastic behaviors. Furthermore, several numerical examples with different cracking modes are studied. The results show that the proposed method provides a robust, effective, and fast way to solve the multiple-crack problems in concrete.

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“…However, it is difficult to find the Lagrange multipliers that satisfy the biorthogonal condition in the XFEM. 34 These issues greatly limit the high efficiency of nonlinear contact analysis in the XFEM, especially for large-scale problems. On the other hand, due to the complexity of geometry, 3D XFEM contact problems have not been studied as much as 2D problems.…”

Section: Introductionmentioning

confidence: 99%

“…The dual mortar method provides a static condensation of Lagrange multipliers to avoid the increased system size and the nonpositive defined property. However, it is difficult to find the Lagrange multipliers that satisfy the biorthogonal condition in the XFEM 34 . These issues greatly limit the high efficiency of nonlinear contact analysis in the XFEM, especially for large‐scale problems.…”

Section: Introductionmentioning

confidence: 99%

A virtual interface‐coupled extended finite element method for three‐dimensional contact problems

Fang

Zhang

Zhou

et al. 2020

Numerical Meth Engineering

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In this article, we propose a virtual interface-coupled technique to model the arbitrary discontinuous interface based on the three-field dual mortar method. The computational domain is divided into several subdomains and the enriched nodes are individually introduced to construct the approximation of the displacement field. This method provides a flexible way to describe the multiple-body contact with nonconforming mesh in the extended finite element method (XFEM). An independent virtual interface is employed to replace the XFEM discontinuous interface. The connect condition between the virtual interface and discontinuous interface is imposed using the dual Lagrange multiplier method. Due to the bi-orthogonality condition, the Lagrange multipliers can be locally eliminated at a very low computational cost. The resulting system matrix is symmetric positive definite and well-conditioned. Furthermore, the contact and natural boundary conditions can be directly imposed on the virtual interface. Several numerical experiments are performed and the results show that the proposed method provides an effective, robust, and fast way to simulate three-dimensional contact behaviors of nonconforming interfaces.

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A contact algorithm for cohesive cracks in the extended finite element method

Cited by 16 publications

References 43 publications

Analysis of Crack Formation and Growth in Tunnel Linings Using Double-K Fracture Criterion

Analysis of Crack Formation and Growth in Tunnel Linings Using Double-K Fracture Criterion

A numerical algorithm for multiple cracks propagation in concrete structure

A virtual interface‐coupled extended finite element method for three‐dimensional contact problems

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