Dave Martin^a,b,† , Hicham Chaouki^a,b, Jean-Loup Robert^a, Donald Ziegler^c, Mario Fafard^a,b

Frontiers in Heat and Mass Transfer, Vol.7, pp. 1-9, 2016, DOI:10.5098/hmt.7.31

Abstract The two dimensional phase change problem was solved using the extended finite element method with a Lagrange formulation to apply the interface boundary condition. The Lagrange multiplier space is identical to the solution space and does not require stabilization. The solid-liquid interface velocity is determined by the jump in heat flux across the i nterface. Two methods to calculate the jump are used and c ompared. The first is based on an averaged temperature gradient near the interface. The second uses the Lagrange multiplier values to evaluate the jump. The Lagrange multiplier based approach was shown to be more robust… More >

Dave Martin^a,b,† , Hicham Chaouki^a,b, Jean-Loup Robert^a, Donald Ziegler^c, Mario Fafard^a,b

Frontiers in Heat and Mass Transfer, Vol.7, pp. 1-11, 2016, DOI:10.5098/hmt.7.40

Abstract A two phase model for two-dimensional solidification problems with variable densities was developed by coupling the Stefan problem with the Stokes problem and applying a mass conserving velocity condition on the phase change interface. The extended finite element method (XFEM) was used to capture the strong discontinuity of the velocity and pressure as well as the jump in heat flux at the i nterface. The melting temperature and velocity condition were imposed on the interface using a Lagrange multiplier and the penalization method, respectively. The resulting formulations were then coupled using a fixed point iteration a lgorithm. Three examples were… More >

Dave Martin^a,b,† , Hicham Chaouki^a,b, Jean-Loup Robert^a , Donald Ziegler^c , Mario Fafard^a,b

Frontiers in Heat and Mass Transfer, Vol.10, pp. 1-11, 2018, DOI:10.5098/hmt.10.18

Abstract A model for two dimensional solidification problems including convection was developed by coupling the Stefan problem with the Stokes problem. The extended finite element method (XFEM) was used to capture the strong discontinuity in velocity and pressure as well as the jump in heat flux at the phase change interface. The melting temperature and no-slip condition were imposed on the interface using a Lagrange multiplier and the penalization method, respectively. The resulting formulations were then coupled using a fixed point iteration algorithm. The model was able to reproduce the benchmark simulations while maintaining a sharp phase change interface. More >

Zongying Fu¹, Yongdong Zhou¹, Tingguo Yan², Yun Lu^1,*

Journal of Renewable Materials, Vol.11, No.1, pp. 93-102, 2023, DOI:10.32604/jrm.2023.021808

Abstract Drying crack is a common phenomenon occurring during moisture discharge from wood, reducing efficient wood utilization. Drying crack is primarily caused by drying stress, and the reasonable methods for determining drying stress are sparse. In this study, the initiation and propagation of cracks during wood discs drying were simulated using the extended finite element method (XFEM). The distribution of drying stress and displacement was analyzed at different crack conditions based on the simulation results. This study aimed to solve the problem of the limitation of drying stress testing methods and provide a new idea for the study of wood drying… More >

Fang Shi^1,*, Daobing Wang², Xiaogang Chen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 575-598, 2021, DOI:10.32604/cmes.2021.015384

Abstract Field data suggests that carbonate reservoirs contain abundant natural fractures and cavities. The propagation mechanisms of hydraulic fractures in fracture-cavity reservoirs are different from conventional reservoirs on account of the stress concentration surrounding cavities. In this paper, we develop a fully coupled numerical model using the extended finite element method (XFEM) to investigate the behaviors and propagation mechanisms of hydraulic fractures in fracture-cavity reservoirs. Simulation results show that a higher lateral stress coefficient can enhance the influence of the natural cavity, causing a more curved fracture path. However, lower confining stress or smaller in-situ stress difference can reduce this influence,… More >

Pengfei Zhu¹, Qinghui Zhang^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.1, pp. 107-127, 2020, DOI:10.32604/cmes.2020.09831

Abstract There are several difficulties in generalized/extended finite element methods (GFEM/XFEM) for moving interface problems. First, the GFEM/XFEM may be unstable in a sense that condition numbers of system matrices could be much bigger than those of standard FEM. Second, they may not be robust in that the condition numbers increase rapidly as interface curves approach edges of meshes. Furthermore, time stepping schemes need carrying out carefully since both enrichment functions and enriched nodes in the GFEM/XFEM vary in time. This paper is devoted to proposing the stable and robust GFEM/XFEM with effi- cient time stepping schemes for the parabolic interface… More >

Zhongmin Xiao¹, Wengang Zhang², Yanmei Zhang^{1, *}, Mu Fan³

CMC-Computers, Materials & Continua, Vol.62, No.1, pp. 267-280, 2020, DOI:10.32604/cmc.2020.06567

Abstract Fluctuated loadings from currents, waves and sea ground motions are observed on offshore steel pipelines, and they will result in small cracks to propagate continuously and cause unexpected damage to offshore/geotechnical infrastructures. In spite of the availability of efficient techniques and high-power computers for solving crack problems, investigations on the fatigue life of offshore pipelines with 3D interacting cracks are still rarely found in open literature. In the current study, systematic numerical investigations are performed on fatigue crack growth behaviours of offshore pipelines containing coplanar and non-coplanar cracks. Extended finite element method (XFEM) is adopted to simulate the fatigue crack… More >

Yana Wang^1,2,3,4, Ruodi Jia^1,5, Fengrui Liu^1,5,6,*

CMES-Computer Modeling in Engineering & Sciences, Vol.120, No.1, pp. 215-234, 2019, DOI:10.32604/cmes.2019.06542

Abstract Delamination and matrix cracking are two common failure mechanisms in composite structures, and are usually coupled with each other, leading to multiple failures pattern. This paper proposed a fast damage prediction methodology for composite laminated structures based on the ply-by-ply 2D (two dimensional) FE model of composite laminates in the transverse plane. The layer-wise 2D FE model was firstly used in conjunction with the integrated XFEM/CE strategy, which simulated the interface delamination with cohesive elements and the intra-ply matrix crack with XFEM (extended finite element method). To realize ply-by-ply 2D FE (finite element) modeling of composite laminates, two 2D material… More >

Xue-cong Liu¹, Qing Zhang^1,2, Xiao-zhou Xia¹

CMES-Computer Modeling in Engineering & Sciences, Vol.113, No.4, pp. 411-427, 2017, DOI:10.3970/cmes.2017.113.411

Abstract The manuscript titled “The Stable Explicit Time Stepping Analysis with a New Enrichment Scheme by XFEM,” has been retracted from the Computer Modeling in Engineering & Sciences (CMES), vol. 113, no. 4. Retraction of this article is made upon the request of the authors, Xue-cong Liu, Qing Zhang, and Xiao-zhou Xia. The authors submitted their manuscript on October 7, 2017, and the authors later made a separate request to withdraw their submission when it was still being reviewed. Due to the glitches of the old submission system and failed communications between the managing editor and the corresponding author, the withdraw… More >

Leiting Dong^1,2, Satya N. Atluri^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.5, pp. 379-413, 2013, DOI:10.3970/cmes.2013.090.379

Abstract The SGBEM-FEM alternating method is compared with the recently popularized XFEM, for analyzing mixed-mode fracture and fatigue growth of 3D nonplanar cracks in complex solid and structural geometries. A large set of 3D examples with different degrees of complexity is analyzed by the SGBEM-FEM alternating method, and the numerical results are compared with those obtained by XFEM available in the open literature. It is clearly shown that: (a) SGBEM-FEM alternating method gives extremely high accuracy for the stress intensity factors; but the XFEM gives rather poor computational results, even for the most simple 3D cracks; (b) while SGBEM-FEM alternating method… More >