Numerical simulation of 2-D weak and strong discontinuities by a novel approach based on XFEM with local mesh refinement

Published on Feb 1, 2018in Computers & Structures3.664
· DOI :10.1016/J.COMPSTRUC.2017.11.007
Tiantang Yu32
Estimated H-index: 32
(Hohai University),
Tinh Quoc Bui54
Estimated H-index: 54
(TITech: Tokyo Institute of Technology)
Sources
Abstract
Abstract The present paper is concerned with numerical simulation of two-dimensional (2-D) cracks and material interfaces by an effective computational approach. A local mesh refinement in terms of extended finite element method is thus described. The new approach combines a posteriori error estimation algorithm, a local non-conformal mesh connection strategy, and local enrichment. An error estimator based on recovery strain for adaptivity is used; allowing the mesh where it is needed is subsequently refined. Unlike preceding local refined methods, variable-node elements are integrated into the present formulation instead, which aims to treat mismatching problem induced by different scale-meshes in an effective way. The discontinuity and singularity of cracks or material interfaces are captured by local enrichments in terms of partition of unity. Due to existence of different types of elements in the model, a special technique is thus proposed for appropriately and accurately treating numerical integration. We address the developed methodology, assessing its numerical properties and performance through several numerical examples. In particular, discontinuity problems with material interfaces, multiple inclusions, single and multiple cracks are analyzed. The obtained results indicate a high accuracy, low cost and good performance of the proposed method in simulation of 2-D cracks and material interfaces.
📖 Papers frequently viewed together
67 Citations
4,357 Citations
2,659 Citations
References51
Newest
#1Zuoyi Kang (TITech: Tokyo Institute of Technology)H-Index: 3
#2Tinh Quoc Bui (TITech: Tokyo Institute of Technology)H-Index: 54
Last. Sohichi Hirose (TITech: Tokyo Institute of Technology)H-Index: 16
view all 4 authors...
Abstract The recently developed local enriched consecutive-interpolation 4-node quadrilateral element (XCQ4) is extended to study transient dynamic stress intensity factors (DSIFs) for isotropic solids and anisotropic composite materials containing stationary cracks. The XCQ4 involves both nodal values and averaged nodal gradients as interpolation conditions to smooth the distribution of unknown variables. The possible physical properties of enriched nodes in consecutive-interpolation procedure ...
32 CitationsSource
#1Zhen Wang (Hohai University)H-Index: 2
#2Tiantang Yu (Hohai University)H-Index: 32
Last. Jose L. Curiel-Sosa (University of Sheffield)H-Index: 14
view all 7 authors...
Abstract A novel local mesh refinement approach for fracture analysis of three-dimensional (3-D) linear elastic solids is developed, considering both 3-D straight and curved planar cracks. The present local mesh refinement formulation is a combination of the extended finite element method (XFEM), variable-node hexahedron elements, and a posteriori error indicator. Our 3-D formulation using hexahedron elements rigorously embraces a posteriori error estimation scheme, a structural coupling scale-m...
67 CitationsSource
#1Tinh Quoc Bui (TITech: Tokyo Institute of Technology)H-Index: 54
#2Sohichi Hirose (TITech: Tokyo Institute of Technology)H-Index: 15
Last. Jun Lei (Beijing University of Technology)H-Index: 11
view all 7 authors...
Abstract A dynamic extended isogeometric analysis (XIGA) is developed for transient fracture of cracked magnetoelectroelastic (MEE) solids under coupled electro-magneto-mechanical loading, taking the advantages of high order NURBS basis functions and enrichment methods. The extended dynamic fracture parameters are estimated through the electro-magneto-mechanical interaction integral. Numerical examples of electrically and magnetically impermeable cracks are studied to demonstrate the accuracy of...
94 CitationsSource
Abstract Accurate numerical modeling of multifield piezoelectric materials is challenging because of the inherent electro-mechanical coupling effect and material anisotropic behaviors. The modeling becomes even more difficult especially for problems with non-smooth solutions like crack under dynamic loading. We present in this paper an extension of the extended isogeometric analysis (XIGA) for simulation of two-dimensional fracture mechanics problems in piezoelectric materials under dynamic and ...
128 CitationsSource
#1Tiantang Yu (Hohai University)H-Index: 32
#2Tinh Quoc Bui (TITech: Tokyo Institute of Technology)H-Index: 54
Last. Sohichi Hirose (TITech: Tokyo Institute of Technology)H-Index: 15
view all 5 authors...
Interfacial dynamic impermeable cracks analysis of dissimilar piezoelectric solids under coupled electromechanical impact loadings by the extended finite element method (X-FEM) is presented. The dynamic X-FEM approach recently developed by the authors is further extended to analyze transient responses of interfacial impermeable cracks in dissimilar piezoelectric structures. The mechanical displacements and electrical potential are approximated by appropriate enrichment functions that are not onl...
62 CitationsSource
#1Luyang Shi (Hohai University)H-Index: 1
#2Tiantang Yu (Hohai University)H-Index: 32
Last. Tinh Quoc Bui (TITech: Tokyo Institute of Technology)H-Index: 54
view all 3 authors...
A numerical model based on the extended finite element method (XFEM) is developed to serve this purpose. The present approach involves several features of an effective numerical tool in modelling hydraulic fracturing: the generalized shape functions are used in a cluster of nodes around the cracks, whereas the conventional finite element shape functionsare applied outside the cracks; the ramp function is introduced to remove the blending elements in the XFEM setting; and the contact conditions b...
24 CitationsSource
#2Juan José Ródenas (Polytechnic University of Valencia)H-Index: 18
Last. F. J. Fuenmayor (Polytechnic University of Valencia)H-Index: 21
view all 6 authors...
Novel goal-oriented error estimator for LEFM problems solved with XFEM.Enhanced recovery technique with equilibrium conditions and stress splitting.Dual problem is formulated for the stress intensity factor in a new way.We report convergence and a notable improvement of the effectivity index. Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of finite element numerical simulations that involve complex domains. By locally improving the ...
23 CitationsSource
#1Xiaodong ZhangH-Index: 2
#2Tinh Quoc Bui (TITech: Tokyo Institute of Technology)H-Index: 54
Purpose – The purpose of this paper is to achieve numerical simulation of cohesive crack growth in concrete structures. Design/methodology/approach – The extended finite element method (XFEM) using four-node quadrilateral element associated with the fictitious cohesive crack model is used. A mixed-mode traction-separation law is assumed for the cohesive crack in the fracture process zone (FPZ). Enrichments are considered for both partly and fully cracked elements, and it thus makes the evolution...
66 CitationsSource
#1Peng Liu (Hohai University)H-Index: 12
#2Tiantang Yu (Hohai University)H-Index: 32
Last. C.W. Lim (CityU: City University of Hong Kong)H-Index: 63
view all 6 authors...
Transient thermal dynamic analysis of stationary cracks in functionally graded piezoelectric materials (FGPMs) based on the extended finite element method (X-FEM) is presented. Both heating and cooling shocks are considered. The material properties are supposed to vary exponentially along specific direction while the crack-faces are assumed to be adiabatic and electrically impermeable. A dynamic X-FEM model is developed in which both Crank–Nicolson and Newmark time integration methods are used f...
88 CitationsSource
#1A. Apostolatos (TUM: Technische Universität München)H-Index: 6
#2R. Schmidt (TUM: Technische Universität München)H-Index: 4
Last. Kai-Uwe Bletzinger (TUM: Technische Universität München)H-Index: 32
view all 4 authors...
This paper provides a detailed elaboration and assessment of the most common domain decomposition methods for their application in isogeometric analysis. The methods comprise a penalty approach, Lagrange multiplier methods, and a Nitsche-type method. For the Nitsche method, a new stabilized formulation is developed in the context of isogeometric analysis to guarantee coercivity. All these methods are investigated on problems of linear elasticity and eigenfrequency analysis in 2D. In particular, ...
122 CitationsSource
Cited By55
Newest
#1S.Z. Feng (HEBUT: Hebei University of Technology)H-Index: 2
#2Xu Han (HEBUT: Hebei University of Technology)H-Index: 61
Last. Atilla Incecik (University of Strathclyde)H-Index: 28
view all 4 authors...
Abstract null null An effective approach is proposed to predict the remaining fatigue life (RFL) of structures with stochastic parameters. The extended finite element method (XFEM) was firstly used to produce a large amount of datasets associated with structural responses and RFL. Then, a RFL prediction model was developed using the ensemble learning algorithm, which employed multiple machine-learning algorithms to learn useful degradation patterns of the structures from the XFEM datasets. Sever...
Source
#2Rolf MahnkenH-Index: 19
Last. Y. Xu
view all 4 authors...
Source
#1Shuohui Yin (XTU: Xiangtan University)H-Index: 18
#2Ning Zhang (XTU: Xiangtan University)
Last. Yu Cong (Université Paris-Saclay)
view all 0 authors...
Abstract null null This paper aims to develop a variable-node multiscale extended finite element method (V-XFEM) for dynamic fracture analysis of the linearly uncoupled and coupled physical phenomena in a compact formula. The general governing equations for the linearly uncoupled and coupled physical phenomena are presented in a compact form. The local mesh refinement technique for modeling cracks is used to improve the accuracy and efficiency, in which variable-node elements without modifying t...
Source
#1S.Z. Feng (HEBUT: Hebei University of Technology)H-Index: 2
#2Y. Xu (Ocean University of China)
Last. Atilla Incecik (University of Strathclyde)H-Index: 28
view all 5 authors...
Abstract In this work, we proposed a novel approach for the prediction of residual useful life (RUL) of structures through appropriately combining the phase field method and deep-learning. In this new approach, the phase field method is firstly utilized to obtain the structural responses of crack growth, which are further preserved as images. Then, the convolutional neural network (CNN) is constructed to establish a predictive model . The proposed approach is a hybrid model of both physical and ...
1 CitationsSource
This article is presented to investigate the influence of several discontinuity like interfacial-crack, void and inclusion in the bimaterial plate, to analyze the normalized mixed-mode stress inten...
Source
#1Shouyan Jiang (Hohai University)
#2Zhao Linxin (Hohai University)
Last. Chengbin Du (Hohai University)
view all 3 authors...
Source
#1Raphael Suda (TU Wien: Vienna University of Technology)H-Index: 1
#2Thomas Kiefer (TU Wien: Vienna University of Technology)H-Index: 5
Last. Josef Füssl (TU Wien: Vienna University of Technology)H-Index: 16
view all 4 authors...
Abstract Since lateral tensile stresses trigger failure of vertically perforated clay block masonry under vertical loading, reinforcement of the bed joints introduces a new way to improve the vertical resistance of masonry. The aim of this work is to estimate the feasible increase of the vertical compressive strength by means of the eXtended Finite Element Method (XFEM). Using a unit cell approach and a stochastic strength distribution, the increase of the masonry strength’s 5%-quantile could be...
Source
#1Zhang Ying (SWPU: Southwest Petroleum University)
#2Lian Zhang-hua (SWPU: Southwest Petroleum University)H-Index: 1
Last. Nguejio Florent Brice (SUSE: Sichuan University of Science and Engineering)
view all 4 authors...
In this paper, the process of crack propagation is investigated using the extended finite element method at the mesoscale to study the drill pipe fracture mechanism. Firstly, the property of the S135 drill pipe was analyzed through physical and chemical experiments and the scanning electron microscope method. After that, a grain distribution model of the drill pipe material at the mesoscale was established by the Python scripting language on ABAQUS platform. Furthermore, the extended finite elem...
Source
#1Hongting Yuan (Hohai University)H-Index: 2
#2Tiantang Yu (Hohai University)H-Index: 32
Last. Tinh Quoc Bui (TITech: Tokyo Institute of Technology)H-Index: 54
view all 3 authors...
Abstract The objective of this article is to simulate crack growth of complex Mindlin–Reissner plates by developing an adaptive multi-patch extended isogeometric analysis (XIGA). Nitsche’s method is used to treat continuity between multi-patches or the coupling of non-conforming meshes, exactly describing the geometry of complex plates. The computational meshes in XIGA are independent of the cracks by introducing some enrichment functions into the displacement approximation based on the partitio...
2 CitationsSource
1 CitationsSource