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Article
Publication date: 1 January 1989

M.J. Panthaki, J.F. Abel and P.A. Wawrzynek

An important objective of 3‐D graphical finite element postprocessing is the facility to indicate to the engineer the accuracy of analysis results. The inclusion of mesh quality…

27

Abstract

An important objective of 3‐D graphical finite element postprocessing is the facility to indicate to the engineer the accuracy of analysis results. The inclusion of mesh quality sensors permits a subjective evaluation of the adequacy of a single analysis being interpreted. For graphical approaches, both strain energy density gradients and discontinuities of unsmoothed responses and their gradients have proved to be effective sensors. Interactive graphical tools which can display discontinuity information effectively are described; these are essentially different from the ordinary methods used for the viewing of smoothed results.

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Engineering Computations, vol. 6 no. 1
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 February 1998

C. Koenke, R. Harte, W.B. Krätzig and O. Rosenstein

The simulation of fracture processes for discrete crack propagation is well established for linear‐elastic cracking problems. Applying finite element techniques for the numerical…

849

Abstract

The simulation of fracture processes for discrete crack propagation is well established for linear‐elastic cracking problems. Applying finite element techniques for the numerical formulation, at every incremental macro‐crack step the element mesh has to be adapted such that the crack path remains independent of the initial mesh. The accuracy of the obtained results has to be controlled by suitable error estimators and error indicators. Considering the dependence of the predicted crack path on the precision of the displacement and stress computation, quality measures for the computed results are recommended. In this research the use of the Babuska/Rheinboldt error indicator in combination with linear‐elastic crack propagation problems is demonstrated. Based on this error measure an adaptive mesh refinement technique is developed. In comparison with classical discrete crack propagation simulations the advantages of the new concept can be clearly observed.

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Engineering Computations, vol. 15 no. 1
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 February 1996

Jaroslav Mackerle

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included…

677

Abstract

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.

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Engineering Computations, vol. 13 no. 1
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 24 February 2012

Juha Kuutti and Kari Kolari

The purpose of this paper is to present a new simplified local remeshing procedure for the study of discrete crack propagation in finite element (FE) mesh. The proposed technique…

757

Abstract

Purpose

The purpose of this paper is to present a new simplified local remeshing procedure for the study of discrete crack propagation in finite element (FE) mesh. The proposed technique accounts for the generation and propagation of crack‐like failure within an FE‐model. Beside crack propagation, the technique enables the analysis of fragmentation of initially intact continuum. The capability of modelling fragmentation is essential in various structure‐structure interaction analyses such as projectile impact analysis and ice‐structure interaction analysis.

Design/methodology/approach

The procedure combines continuum damage mechanics (CDM), fictitious crack approach and a new local remeshing procedure. In the approach a fictitious crack is replaced by a discrete crack by applying delete‐and‐fill local remeshing. The proposed method is independent of mesh topology unlike the traditional discrete crack approach. The procedure is implemented for 3‐D solid elements in commercial finite element software Abaqus/Explicit using Python scripting. The procedure is completely automated, such that crack initiation and propagation analyses do not require user intervention. A relatively simple constitutive model was implemented strictly for demonstrative purposes.

Findings

Well known examples were simulated to verify the applicability of the method. The simulations revealed the capabilities of the method and reasonable correspondence with reference results was obtained. Material fragmentation was successfully simulated in ice‐structure interaction analysis.

Originality/value

The procedure for modelling discrete crack propagation and fragmentation of initially intact quasi‐brittle materials based on local remeshing has not been presented previously. The procedure is well suited for simulation of fragmentation and is implemented in a commercial FE‐software.

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Article
Publication date: 1 March 1999

C.K. Lee

A new mesh generation procedure is suggested for the generation of 2D adaptive finite element meshes with strong element gradation and stretching effects. Metric tensors are…

652

Abstract

A new mesh generation procedure is suggested for the generation of 2D adaptive finite element meshes with strong element gradation and stretching effects. Metric tensors are employed to define and control the element characteristics during the mesh generation process. By using the metric tensor specification and a new, robust and refined advancing front triangulation kernel, triangles with nearly unit edge length with respect to the normalized space are generated. Highly graded and stretched elements can be generated without much difficulty and the operation complexity of the mesh generation process is exactly the same as the usual 2D advancing front mesh generator. A set of mesh quality enhancement procedures has also been suggested for the further improvement of the quality of the finite element meshes. A simple and effective mesh conversion scheme is used to convert the output triangular mesh to a pure quadrilateral mesh while all the essential element characteristics are preserved. Mesh generation examples show that high quality finite element meshes with element characteristics compatible with the specified metric tensors are generated within a reasonable time limit in a common small computing environment.

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Engineering Computations, vol. 16 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 24 August 2018

Bin Chen, Song Cen, Andrew R. Barron, D.R.J. Owen and Chenfeng Li

The purpose of this paper is to systematically investigate the fluid lag phenomena and its influence in the hydraulic fracturing process, including all stages of fluid-lag…

1175

Abstract

Purpose

The purpose of this paper is to systematically investigate the fluid lag phenomena and its influence in the hydraulic fracturing process, including all stages of fluid-lag evolution, the transition between different stages and their coupling with dynamic fracture propagation under common conditions.

Design/methodology/approach

A plane 2D model is developed to simulate the complex evolution of fluid lag during the propagation of a hydraulic fracture driven by an impressible Newtonian fluid. Based on the finite element method, a fully implicit solution scheme is proposed to solve the strongly coupled rock deformation, fluid flow and fracture propagation. Using the proposed model, comprehensive parametric studies are performed to examine the evolution of fluid lag in various geological and operational conditions.

Findings

The numerical simulations predict that the lag ratio is around 5% or even lower at the beginning stage of hydraulic fracture under practical geological conditions. With the fracture propagation, the lag ratio keeps decreasing and can be ignored in the late stage of hydraulic fracturing for typical parameter combinations. On the numerical aspect, whether the fluid lag can be ignored depends not only on the lag ratio but also on the minimum mesh size used for fluid flow. In addition, an overall mixed-mode fracture propagation factor is proposed to describe the relationship between diverse parameters and fracture curvature.

Research limitations/implications

In this study, relatively simple physical models such as linear elasticity for solid, Newtonian model for fluid and linear elasticity fracture mechanics for fracture are used. The current model does not account for such effects like leak off, poroelasticity and softening of rock formations, which may also visibly affect the fluid lag depending on specific reservoir conditions.

Originality/value

This study helps to understand the effect of fluid lag during hydraulic fracturing processes and provides numerical experience in dealing with the fluid lag with finite element simulation.

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Engineering Computations, vol. 35 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 April 2022

Can Ban, Na Na Pu, Yi Fei Zhang and Ma Wentao

This article aims to develop an accurate and efficient meshfree Galerkin method based on the strain smoothing technique for linear elastic continuous and fracture problems.

125

Abstract

Purpose

This article aims to develop an accurate and efficient meshfree Galerkin method based on the strain smoothing technique for linear elastic continuous and fracture problems.

Design/methodology/approach

This paper proposed a generalized linear smoothed meshfree method (LSMM), in which the compatible strain is reconstructed by the linear smoothed strains. Based on the idea of the weighted residual method and employing three linearly independent weight functions, the linear smoothed strains can be created easily in a smoothing domain. Using various types of basic functions, LSMM can solve the linear elastic continuous and fracture problems in a unified way.

Findings

On the one hand, the LSMM inherits the properties of high efficiency and stability from the stabilized conforming nodal integration (SCNI). On the other hand, the LSMM is more accurate than the SCNI, because it can produce continuous strains instead of the piece-wise strains obtained by SCNI. Those excellent performances ensure that the LSMM has the capability to precisely track the crack propagation problems. Several numerical examples are investigated to verify the accurate, convergence rate and robustness of the present LSMM.

Originality/value

This study provides an accurate and efficient meshfree method for simulating crack growth.

Details

Engineering Computations, vol. 39 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 13 March 2020

Zhiqiang Xie, Lei Wang, Zhengyang Zhu, Zhi Fu and Xingdong Lv

The purpose of this paper is to introduce an interval finite element method (IFEM) to simulate the temperature field of mass concrete under multiple influence uncertainties e.g…

115

Abstract

Purpose

The purpose of this paper is to introduce an interval finite element method (IFEM) to simulate the temperature field of mass concrete under multiple influence uncertainties e.g. environmental temperature, material properties, pouring construction and pipe cooling.

Design/methodology/approach

Uncertainties of the significant factors such as the ambient temperature, the adiabatic temperature rise, the placing temperature and the pipe cooling are comprehensively studied and represented as the interval numbers. Then, an IFEM equation is derived and a method for obtaining interval results based on monotonicity is also presented. To verify the proposed method, a non-adiabatic temperature rise test was carried out and subsequently simulated with the method. An excellent agreement is achieved between the simulation results and the monitoring data.

Findings

An IFEM method is proposed and a non-adiabatic temperature rise test is simulated to verify the method. The interval results are discussed and compared with monitoring data. The proposed method is found to be feasible and effective.

Originality/value

Compared with the traditional finite element methods, the proposed method taking the uncertainty of various factors into account and it will be helpful for engineers to gain a better understanding of the real condition.

Details

Engineering Computations, vol. 37 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 30 September 2021

Marcel Xavier and Nicolas Van Goethem

In the paper an approach for crack nucleation and propagation phenomena in brittle plate structures is presented.

50

Abstract

Purpose

In the paper an approach for crack nucleation and propagation phenomena in brittle plate structures is presented.

Design/methodology/approach

The Francfort–Marigo damage theory is adapted to the Kirchhoff and Reissner–Mindlin plate bending models. Then, the topological derivative method is used to minimize the associated Francfort–Marigo shape functional. In particular, the whole damaging process is governed by a threshold approach based on the topological derivative field, leading to a notable simple algorithm.

Findings

Numerical simulations are driven in order to verify the applicability of the proposed method in the context of brittle fracture modeling on plates. The obtained results reveal the capability of the method to determine nucleation and propagation including bifurcation of multiple cracks with a minimal number of user-defined algorithmic parameters.

Originality/value

This is the first work concerning brittle fracture modeling of plate structures based on the topological derivative method.

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Article
Publication date: 2 August 2023

Aurojyoti Prusty and Amirtham Rajagopal

This study implements the fourth-order phase field method (PFM) for modeling fracture in brittle materials. The weak form of the fourth-order PFM requires C1 basis functions for…

133

Abstract

Purpose

This study implements the fourth-order phase field method (PFM) for modeling fracture in brittle materials. The weak form of the fourth-order PFM requires C1 basis functions for the crack evolution scalar field in a finite element framework. To address this, non-Sibsonian type shape functions that are nonpolynomial types based on distance measures, are used in the context of natural neighbor shape functions. The capability and efficiency of this method are studied for modeling cracks.

Design/methodology/approach

The weak form of the fourth-order PFM is derived from two governing equations for finite element modeling. C0 non-Sibsonian shape functions are derived using distance measures on a generalized quad element. Then these shape functions are degree elevated with Bernstein-Bezier (BB) patch to get higher-order continuity (C1) in the shape function. The quad element is divided into several background triangular elements to apply the Gauss-quadrature rule for numerical integration. Both fourth-order and second-order PFMs are implemented in a finite element framework. The efficiency of the interpolation function is studied in terms of convergence and accuracy for capturing crack topology in the fourth-order PFM.

Findings

It is observed that fourth-order PFM has higher accuracy and convergence than second-order PFM using non-Sibsonian type interpolants. The former predicts higher failure loads and failure displacements compared to the second-order model due to the addition of higher-order terms in the energy equation. The fracture pattern is realistic when only the tensile part of the strain energy is taken for fracture evolution. The fracture pattern is also observed in the compressive region when both tensile and compressive energy for crack evolution are taken into account, which is unrealistic. Length scale has a certain specific effect on the failure load of the specimen.

Originality/value

Fourth-order PFM is implemented using C1 non-Sibsonian type of shape functions. The derivation and implementation are carried out for both the second-order and fourth-order PFM. The length scale effect on both models is shown. The better accuracy and convergence rate of the fourth-order PFM over second-order PFM are studied using the current approach. The critical difference between the isotropic phase field and the hybrid phase field approach is also presented to showcase the importance of strain energy decomposition in PFM.

Details

Engineering Computations, vol. 40 no. 6
Type: Research Article
ISSN: 0264-4401

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