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A FEniCS implementation of the phase field method for quasi-static brittle fracture

HIRSHIKESH, Sundararajan NATARAJAN, Ratna Kumar ANNABATTULA

Frontiers of Structural and Civil Engineering 2019, Volume 13, Issue 2,   Pages 380-396 doi: 10.1007/s11709-018-0471-9

Abstract: In the recent years, the phase field method for simulating fracture problems has received considerable attention. This is due to the salient features of the method: 1) it can be incorporated into any conventional finite element software; 2) has a scalar damage variable is used to represent the discontinuous surface implicitly and 3) the crack initiation and subsequent propagation and branching are treated with less complexity. Within this framework, the linear momentum equations are coupled with the diffusion type equation, which describes the evolution of the damage variable. The coupled nonlinear system of partial differential equations are solved in a ‘staggered’ approach. The present work discusses the implementation of the phase field method for brittle fracture within the open-source finite element software, FEniCS. The FEniCS provides a framework for the automated solutions of the partial differential equations. The details of the implementation which forms the core of the analysis are presented. The implementation is validated by solving a few benchmark problems and comparing the results with the open literature.

Keywords： phase field method     FEniCS     brittle fracture     crack propagation     variational theory of fracture    

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Peridynamics versus XFEM: a comparative study for quasi-static crack problems

Jinhai ZHAO, Hesheng TANG, Songtao XUE

Frontiers of Structural and Civil Engineering 2018, Volume 12, Issue 4,   Pages 548-557 doi: 10.1007/s11709-017-0434-6

Abstract: Peridynamics (PD) is a nonlocal continuum theory based on integro-differential equations without spatial derivatives. The fracture criterion is implicitly incorporated in the PD theory and fracture is a natural outcome of the simulation. However, capturing of complex mixed-mode crack patterns has been proven to be difficult with PD. On the other hand, the extended finite element method (XFEM) is one of the most popular methods for fracture which allows crack propagation with minimal remeshing. It requires a fracture criterion which is independent of the underlying discretization though a certain refinement is needed in order to obtain suitable results. This article presents a comparative study between XFEM and PD. Therefore, two examples are studied. The first example is crack propagation in a double notched specimen under uniaxial tension with different crack spacings in loading direction. The second example is the specimens with two center cracks. The results show that PD as well as XFEM are well suited to capture this type of behaviour.

Keywords： XFEM     peridynamic     bilateral crack     parallel double cracks     nonlocal theory    

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Seismic response of precast reinforced concrete wall subjected to cyclic in-plane and constant out-of-plane loading

Frontiers of Structural and Civil Engineering 2021, Volume 15, Issue 5,   Pages 1128-1143 doi: 10.1007/s11709-021-0753-5

Abstract: and deformation characteristics governed by its ductile response in the nonlinear phase during the test

Keywords： precast wall     basement wall     out-of-plane response     quasi-static test     sand backfill     seismic parameters    

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life prediction of thin tube using strain energy density as a function of stress triaxiality under quasi-static

Tahir MAHMOOD, Sangarapillai KANAPATHIPILLAI, Mahiuddin CHOWDHURY

Frontiers of Mechanical Engineering 2013, Volume 8, Issue 2,   Pages 181-186 doi: 10.1007/s11465-013-0257-7

Abstract:

This paper demonstrates the application of a new multiaxial creep damage model developed by authors using stress traixiality to predict the failure time of a component made of 0.5%Cr-0.5%Mo-0.25%V low alloy steel. The model employs strain energy density and assumes that the uniaxial strain energy density of a component can be easily calculated and can be converted to multi-axial strain energy density by multiplying it to a function of stress trixiality which is a ratio of mean stress to equivalent stress. For comparison, an elastic-creep and elastic-plastic-creep finite element analysis (FEA) is performed to get multi-axial strain energy density of the component which is compared with the calculated strain energy density for both cases. The verification and application of the model are demonstrated by applying it to thin tube for which the experimental data are available. The predicted failure times by the model are compared with the experimental results. The results show that the proposed model is capable of predicting failure times of the component made of the above-mentioned material with an accuracy of 4.0%.

Keywords： elastic-creep     elastic-plastic-creep     stress triaxiality     life prediction     pressure vessels     finite element analysis (FEA)    

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A Comparative Study of Friction Self-Piercing Riveting and Self-Piercing Riveting of Aluminum Alloy AA5182-O Article

Yunwu Ma,He Shan,Sizhe Niu,Yongbing Li,Zhongqin Lin,Ninshu Ma

Engineering 2021, Volume 7, Issue 12,   Pages 1741-1750 doi: 10.1016/j.eng.2020.06.015

Abstract: carried out to compare the two processes in terms of joint macrogeometry, tooling force, microhardness, quasi-staticbonding enhanced the F-SPR joint stiffness under lap-shear loading, which contributed to the higher quasi-static

Keywords： Self-piercing riveting     Friction self-piercing riveting     Mechanical joining     Quasi-static strength     Fatigue    

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Research on the Quasi-static and Dynamic Properties and Constitutive Relation of Carbon Fiber-reinforced

Zhang Tai,Wang Xiaojun,Wang Zhihai,Guo Yang,Wang Yuanbo

Strategic Study of CAE 2006, Volume 8, Issue 5,   Pages 63-68

Abstract:

The quasi-static and dynamic compression properties of carbon fiber-reinforced phenolic composite

Keywords： carbon fiber-reinforced phenolic composite     dynamic properties     viscoelasticity     constitutive model     time-temperature equivalent law    

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A novel finite element formulation for static bending analysis of functionally graded porous sandwich

Van Chinh NGUYEN; Trung Thanh TRAN; Trung NGUYEN-THOI; Quoc-Hoa PHAM

Frontiers of Structural and Civil Engineering 2022, Volume 16, Issue 12,   Pages 1599-1620 doi: 10.1007/s11709-022-0891-4

Abstract: This article aims to propose a finite element formulation based on Quasi-3D theory for the static bending(Q4) element with nine degrees of freedom (DOFs) per node is derived and employed in analyzing the staticid="mathml_M1" display="inline" overflow="scroll">ξ on the static

Keywords： sandwich plates     functionally graded porous     static bending     Quasi-3D theory     Q4 element    

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Study of in situ test to DX pile and post grouting bored pile

Liu Chungang,Chai Xiaobing,Ouyang Yi,He Dexin

Strategic Study of CAE 2012, Volume 14, Issue 1,   Pages 80-85

Abstract:

The in-situ vertical resisting compression static test of DX pile isand post-grouting bored pile can enhance capacity and control settlement effectively;effect of four test

Keywords： DX pile     static load test     bearing capacity     settlement    

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Experimental and parametrical investigation of pre-stressed ultrahigh-performance fiber-reinforced concrete railway sleepers

Frontiers of Structural and Civil Engineering 2023, Volume 17, Issue 3,   Pages 411-428 doi: 10.1007/s11709-023-0928-3

Abstract: Under European standards, 35 UHPFRC sleepers are subjected to static bending tests at the center and

Keywords： pre-stressed concrete sleeper     ultrahigh performance fiber-reinforced concrete     pull-out test     staticbending test     steel fiber     aspect ratio     volume fraction    

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Free vibration analysis of cracked thin plates by quasi-convex coupled isogeometric-meshfree method

Hanjie ZHANG,Junzhao WU,Dongdong WANG

Frontiers of Structural and Civil Engineering 2015, Volume 9, Issue 4,   Pages 405-419 doi: 10.1007/s11709-015-0310-1

Abstract: The free vibration analysis of cracked thin plates via a quasi-convex coupled isogeometric-meshfree methodvector simultaneously offers the consistent isogeometric-meshfree coupling in the coupled region and the quasi-convexThe quasi-convex meshfree shape functions mimic the isogeometric basis function as well as offer the

Keywords： meshfree method     isogeometric analysis     quasi-convex isogeometric-meshfree method     free vibration     cracked    

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Quasi-period Changes of the Operational Parameters for Hot Oil Pipelines

Cui Hui

Strategic Study of CAE 2006, Volume 8, Issue 1,   Pages 51-53

Abstract:

Subjected to the annual changes of the air temperature, the quasi-period rules of the operational

Keywords： hot oil pipeline     air temperature     soil environment     quasi-period    

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Rare-earth separation based on the differences of ionic magnetic moment via quasi-liquid strategy

Frontiers of Chemical Science and Engineering 2023, Volume 17, Issue 10,   Pages 1584-1594 doi: 10.1007/s11705-022-2189-4

Abstract: effect, and finally the magnetic moment differences between paramagnetic and diamagnetic rare earths in quasi-liquidMagnetic separation via quasi-liquid system strategy provides a possibility of the novel, green, and

Keywords： rare earth element     different magnetic moment     magnetic separation     ionic liquid    

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Predictor-corrector algorithm for solving quasi-separated-flow and transient distributed-parameter model

Ping ZHANG, Guoliang DING

Frontiers in Energy 2010, Volume 4, Issue 4,   Pages 535-541 doi: 10.1007/s11708-010-0113-y

Abstract: The successive sub?stitution (SS) method is a suitable approach to solving the transient distributed-parameter model for heat exchangers. However, this method must be enhanced because its convergence heavily depends on the iterative initial pressure. When the iterative initial pressure is improperly assigned, the calculated flow rates become negative values, causing the state parameters to exhibit negative values as well. Therefore, a predictor-corrector algorithm (PCA) is proposed to improve the convergence of the SS method. A predictor is developed to determine an appropriate iterative initial pressure. Total fluid mass is adopted as the convergence criterion of pressure iteration instead of outlet flow rate as is done in the SS method. Convergence analysis and case study of the PCA and SS method are conducted, which show that the PCA has better convergence than the SS method under the same working conditions.

Keywords： algorithm     convergence     heat exchanger     modeling     transient    

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Damage detection in beam-like structures using static shear energy redistribution

Frontiers of Structural and Civil Engineering 2022, Volume 16, Issue 12,   Pages 1552-1564 doi: 10.1007/s11709-022-0903-4

Abstract: In this study, a static shear energy algorithm is presented for the damage assessment of beam-like structuresTherefore, the change in the static shear energy is employed to determine the damage locations in beam-likeThe static shear energy is derived from the spectral factorization of the elementary stiffness matrix

Keywords： damage detection     beam structure     strain energy     static displacement variation     energy damage index    

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Distributed fiber optic monitoring of a CFA pile with a central reinforcement bar bundle

Yi RUI, Nicholas de BATTISTA, Cedric KECHAVARZI, Xiaomin XU, Mei YIN

Frontiers of Structural and Civil Engineering 2021, Volume 15, Issue 1,   Pages 167-176 doi: 10.1007/s11709-020-0581-z

Abstract: distributed fiber optic sensor (DFOS) technology to measure the strain of a continuous flight auger (CFA) testpile with a central reinforcement bar bundle, during a static load test carried out in London.Based on this pile load test, a finite element (FE) analysis was performed using a one-dimensional nonlinear

Keywords： continuous flight auger pile     static load test     central reinforcement bar bundle     distributed fiber optic    

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Title Author Date Type Operation

A FEniCS implementation of the phase field method for quasi-static brittle fracture

HIRSHIKESH, Sundararajan NATARAJAN, Ratna Kumar ANNABATTULA

Journal Article

Peridynamics versus XFEM: a comparative study for quasi-static crack problems

Jinhai ZHAO, Hesheng TANG, Songtao XUE

Journal Article

Seismic response of precast reinforced concrete wall subjected to cyclic in-plane and constant out-of-plane loading

Journal Article

life prediction of thin tube using strain energy density as a function of stress triaxiality under quasi-static

Tahir MAHMOOD, Sangarapillai KANAPATHIPILLAI, Mahiuddin CHOWDHURY

Journal Article

A Comparative Study of Friction Self-Piercing Riveting and Self-Piercing Riveting of Aluminum Alloy AA5182-O

Yunwu Ma,He Shan,Sizhe Niu,Yongbing Li,Zhongqin Lin,Ninshu Ma

Journal Article

Research on the Quasi-static and Dynamic Properties and Constitutive Relation of Carbon Fiber-reinforced

Zhang Tai,Wang Xiaojun,Wang Zhihai,Guo Yang,Wang Yuanbo

Journal Article

A novel finite element formulation for static bending analysis of functionally graded porous sandwich

Van Chinh NGUYEN; Trung Thanh TRAN; Trung NGUYEN-THOI; Quoc-Hoa PHAM

Journal Article

Study of in situ test to DX pile and post grouting bored pile

Liu Chungang,Chai Xiaobing,Ouyang Yi,He Dexin

Journal Article

Experimental and parametrical investigation of pre-stressed ultrahigh-performance fiber-reinforced concrete railway sleepers

Journal Article

Free vibration analysis of cracked thin plates by quasi-convex coupled isogeometric-meshfree method

Hanjie ZHANG,Junzhao WU,Dongdong WANG

Journal Article

Quasi-period Changes of the Operational Parameters for Hot Oil Pipelines

Cui Hui

Journal Article

Rare-earth separation based on the differences of ionic magnetic moment via quasi-liquid strategy

Journal Article

Predictor-corrector algorithm for solving quasi-separated-flow and transient distributed-parameter model

Ping ZHANG, Guoliang DING

Journal Article

Damage detection in beam-like structures using static shear energy redistribution

Journal Article

Distributed fiber optic monitoring of a CFA pile with a central reinforcement bar bundle

Yi RUI, Nicholas de BATTISTA, Cedric KECHAVARZI, Xiaomin XU, Mei YIN

Journal Article