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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (1) : 215-228     https://doi.org/10.1007/s11709-019-0595-6
RESEARCH ARTICLE
Simulation of cohesive crack growth by a variable-node XFEM
Weihua FANG1, Jiangfei WU2, Tiantang YU2(), Thanh-Tung NGUYEN3, Tinh Quoc BUI4,5()
1. Nanjing Automation Institute of Water Conservancy and Hydrology, Nanjing 210012, China
2. Department of Engineering Mechanics, Hohai University, Nanjing 211100, China
3. Laboratory of Solid Structures, University of Luxembourg, Luxembourg L-1359, Luxembourg
4. Institute for Research and Development, Duy Tan University, Da Nang City 550000, Vietnam
5. Department of Civil and Environmental Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
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Abstract

A new computational approach that combines the extended finite element method associated with variable-node elements and cohesive zone model is developed. By using a new enriched technique based on sign function, the proposed model using 4-node quadrilateral elements can eliminate the blending element problem. It also allows modeling the equal stresses at both sides of the crack in the crack-tip as assumed in the cohesive model, and is able to simulate the arbitrary crack-tip location. The multiscale mesh technique associated with variable-node elements and the arc-length method further improve the efficiency of the developed approach. The performance and accuracy of the present approach are illustrated through numerical experiments considering both mode-I and mixed-mode fracture in concrete.

Keywords extended finite element method      cohesive zone model      sign function      crack propagation     
Corresponding Author(s): Tiantang YU,Tinh Quoc BUI   
Just Accepted Date: 28 October 2019   Online First Date: 17 December 2019    Issue Date: 21 February 2020
 Cite this article:   
Weihua FANG,Jiangfei WU,Tiantang YU, et al. Simulation of cohesive crack growth by a variable-node XFEM[J]. Front. Struct. Civ. Eng., 2020, 14(1): 215-228.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-019-0595-6
http://journal.hep.com.cn/fsce/EN/Y2020/V14/I1/215
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Weihua FANG
Jiangfei WU
Tiantang YU
Thanh-Tung NGUYEN
Tinh Quoc BUI
Fig.1  Schematic illustration of the investigated problem: a solid domain containing a crack, in which the process zone exists at the crack tip. (a) A solid domain with a crack; (b) zoom in the region of the cohesive zone.
Fig.2  Schematic representation of a linear cohesive law adopted to this study.
Fig.3  Nodal discontinuous displacement field for the crack-tip element: (a) displacement field at the nodes 1 and 4; (b) the corresponding isoparametric element.
Fig.4  Meshes representation of two different scale elements. The crosshatched lines show one layer of variable node elements.
Fig.5  A schematic illustration for a (4+ k + m)-node element.
Fig.6  Description of the three-point bending test: geometry and boundary conditions.
Fig.7  Three different meshes used to perform the numerical simulation: (a) coarse scale mesh, (b) fine scale mesh, (c) multiscale mesh.
Fig.8  Comparison of the mechanical response between the reference data and the numerical prediction by the present model for different meshes.
mesh level computational time correlation w.r.t (Ref. [47])
coarse scale mesh 118.8 s 5.44%
fine scale mesh 343.6 s 1.50%
multiscale mesh 260.6 s 2.26%
Tab.1  Mode-I fracture test: comparison of the numerical performance for different meshes
Fig.9  Crack propagation for different loadings (a scaling factor of 200 is used to plot this figure). (a) P = 5.529 kN; (b) P = 3.804 kN; (c) P = 1.961 kN; (d) P = 0.238 kN.
Fig.10  Mixed-mode fracture test of a simple supported beam: geometry, and boundary conditions.
Fig.11  Three different meshes used to perform the numerical simulation: (a) coarse scale mesh, (b) fine scale mesh, (c) multiscale mesh.
Fig.12  Propagation of crack for different loadings (scaling factor 160). (a) P = 3.706 kN; (b) P = 3.243 kN; (c) P = 1.898kN; (d) P = 0.457 kN.
Fig.13  Comparison of the final crack paths.
mesh level computational time correlation w.r.t (Ref. [47])
coarse scale mesh 130.27 s 8.3%
fine scale mesh 410.44 s 1.18%
multiscale mesh 300.52 s 1.78%
Tab.2  Mixed-mode fracture test: comparison of the numerical performance for different meshes
Fig.14  Comparison of the load-CMOD curves obtained from the present model with the reference data in Ref. [47].
Fig.15  Two different irregular meshes used to perform the numerical simulation: (a) fine scale mesh; (b) multiscale mesh.
Fig.16  The load-CMOD curves obtained from the present model with two irregular meshes.
Fig.17  Description of the mixed-mode fracture test: geometry, and boundary conditions.
Fig.18  Three  different meshes used to perform the numerical simulation: (a) coarse scale mesh; (b) fine scale mesh; (c) multiscale mesh.
Fig.19  Comparison of the final crack path obtained from different mesh with the reference result in Ref. [47].
Fig.20  Comparison of the mechanical response: load-CMOD curves obtained from different meshes.
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