scholarly journals Combined Visibility and Surrounding Triangles Method for Simulation of Crack Discontinuities in Meshless Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
H. Pirali ◽  
F. Djavanroodi ◽  
M. Haghpanahi
Keyword(s):  
Diffraction Method ◽  
Meshless Methods ◽  
Standard Test ◽  
The Finite Element Method ◽  
Linear Elastic ◽  
Element Free Galerkin ◽  
Elastic Fracture ◽  
Element Free ◽  
Crack Faces ◽  
Good Agreement

In this paper a combined node searching algorithm for simulation of crack discontinuities in meshless methods called combined visibility and surrounding triangles (CVT) is proposed. The element free Galerkin (EFG) method is employed for stress analysis of cracked bodies. The proposed node searching algorithm is based on the combination of surrounding triangles and visibility methods; the surrounding triangles method is used for support domains of nodes and quadrature points generated at the vicinity of crack faces and the visibility method is used for points located on the crack faces. In comparison with the conventional methods, such as the visibility, the transparency, and the diffraction method, this method is simpler with reasonable efficiency. To show the performance of this method, linear elastic fracture mechanics analyses are performed on number of standard test specimens and stress intensity factors are calculated. It is shown that the results are in good agreement with the exact solution and with those generated by the finite element method (FEM).

Application of Extended Element-Free Galerkin Method to Multiple Flaws Under Brittle Fracture Conditions

2008 ◽  
Author(s):  
T. Rabczuk ◽  
B. Bezensek ◽  
S. Bordas
Keyword(s):  
Partition Of Unity ◽  
Central Feature ◽  
Element Free Galerkin Method ◽  
Linear Elastic ◽  
Element Free Galerkin ◽  
Critical Flaw ◽  
Element Free ◽  
Crack Faces ◽  
Crack Paths ◽  
Extended Element

The extended element-free Galerkin (XEFG) method incorporates cracks through partition of unity enrichment of the standard basis functions. Discontinuous functions are added to capture the jump through the crack faces and near-front enrichment is added to capture the asymptotic behaviour in the vicinity of the crack fronts. Depending on the material behaviour, these functions can be of various type. The method can treat initiation, growth and coalescence of cracks seamlessly in both linear elastic and non-linear settings. The method is a powerful tool for modelling and studying crack paths, which are a central feature in the assessment of multiple flaws. The method is applied to the problem of multiple non-aligned flaws in a ferritic plate under cleavage failure. Fracture paths from two non-aligned notches in a plate are modelled. Based on the observations of crack paths the critical flaw alignment distance is established for non-aligned through-wall flaws.

A New Specimen for Measuring the Interfacial Toughness of Al-0.5%Cu Thin Film on Si Substrate

2005 ◽  
Vol 297-300 ◽  
pp. 521-526
Author(s):  
Insu Jeon ◽  
Masaki Omiya ◽  
Hirotsugu Inoue ◽  
Kikuo Kishimoto ◽  
Tadashi Asahina
Keyword(s):  
Thin Film ◽  
The Finite Element Method ◽  
Si Substrate ◽  
Detailed Structure ◽  
Micro Fabrication ◽  
Interfacial Toughness ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Cu Thin Film ◽  
Research Show

A new specimen is proposed to measure the interfacial toughness between the Al-0.5%Cu thin film and the Si substrate. The plain and general micro-fabrication processes are sufficient to fabricate the specimen. With the help of the finite element method and the concepts of the linear elastic fracture mechanics, the detailed structure for this specimen is modeled and evaluated. The results obtained from this research show that the proposed specimen provides efficient and convenient method to measure the interfacial toughness between the Al-Cu thin film and the Si substrate.

Influence of the Interface and Residual Stresses on the Apparent Fracture Toughness of Layered Ceramic Composites Based on Alumina-Zirconia

2014 ◽  
Vol 606 ◽  
pp. 209-212
Author(s):  
Luboš Náhlík ◽  
Bohuslav Máša ◽  
Pavel Hutař
Keyword(s):  
Residual Stresses ◽  
Crack Propagation ◽  
Ceramic Composites ◽  
Layered Composites ◽  
Material Interfaces ◽  
Linear Elastic ◽  
Apparent Fracture Toughness ◽  
Elastic Fracture ◽  
Layered Ceramic ◽  
Good Agreement

This paper deals with the fracture behaviour of layered ceramic composite with residual stresses. The main goal is to investigate the effect of residual stresses and material interfaces on crack propagation by more complex 3D finite element models. The crack behaviour was described by analytical procedures based on linear elastic fracture mechanics (LEFM) and generalized LEFM. The influence of laminate composition with residual stresses on critical values for crack propagation through the laminate interfaces was also determined. Good agreement has been found to exist between numerical results and experimental data. The results obtained can be used for a design of new layered composites with improved resistance against crack propagation.

Estimation of the Crack Propagation Direction of a Crack Touching the Interface between Two Elastic Materials

2007 ◽  
Vol 567-568 ◽  
pp. 225-228 ◽  
Author(s):  
Luboš Náhlík ◽  
Lucie Šestáková ◽  
Pavel Hutař
Keyword(s):  
Crack Propagation ◽  
Protective Coatings ◽  
The Body ◽  
Elastic Behavior ◽  
Layered Composites ◽  
The Finite Element Method ◽  
Elastic Materials ◽  
Linear Elastic ◽  
Composites Materials ◽  
Elastic Fracture

The objective of the paper is to investigate the direction of a further crack propagation from the interface between two elastic materials. The angle of crack propagation changes when the crack passes the interface. The suggested procedure makes it possible to estimate an angle of propagation under which the crack will propagate into the second material. The assumptions of linear elastic fracture mechanics and elastic behavior of the body with interfaces are considered. The finite element method was used for numerical calculations. The results obtained might contribute to a better understanding of the failure of materials with interfaces (e.g. layered composites, materials with protective coatings) and to a more reliable estimation of the service life of such structures.

Welding Heat Transfer Analysis Using Element Free Galerkin Method

2011 ◽  
Vol 410 ◽  
pp. 298-301 ◽  
Author(s):  
Raj Das ◽  
K.S. Bhattacharjee ◽  
S. Rao
Keyword(s):  
Heat Transfer ◽  
Arc Welding ◽  
Heat Transfer Analysis ◽  
The Finite Element Method ◽  
Element Free Galerkin Method ◽  
High Deformation ◽  
New Class ◽  
Element Free Galerkin ◽  
Mesh Less ◽  
Element Free

Mesh-less methods belong to a new class of numerical methods in computational mechanics and offer several advantages over the conventional mesh-based methods. They enable modelling of processes involving high deformation, severe discontinuities (e.g. fracture) and multiple physical processes. These types of situations are usually encountered in arc welding, rendering its modelling suitable via mesh-less methods. In this paper, a mesh-less Element Free Galerkin (EFG) method has been developed to model the heat transfer during welding. The results predicted by the EFG method are found to be in close agreement with those obtained by the finite element method and those observed in welding experiments. This demonstrates the effectiveness and utilities of the EFG method for modelling and understanding the heat transfer processes in arc welding.

Element-Free Galerkin (EFG) Method for Time Fractional Partial Differential Equations

2011 ◽  
Vol 101-102 ◽  
pp. 343-347
Author(s):  
Yong Qing Liu ◽  
Rong Jun Cheng ◽  
Hong Xia Ge
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Time Derivative ◽  
Discrete Equation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Element Free Galerkin ◽  
Element Free ◽  
Caputo Fractional Order Derivative ◽  
Good Agreement

In this paper, the first order time derivative of time fractional partial differential equations are replaced by the Caputo fractional order derivative. We derive the numerical solution of this equation using the Element-free Galerkin (EFG) method. In order to obtain the discrete equation, a various method is used and the essential boundary conditions are enforced by the penalty method. Numerical examples are presented and the results are in good agreement with exact solutions.

scholarly journals A New Meshless “Fragile Points Method (FPM)” Based on a Galerkin Weak-Form for 2D Flexoelectric Analysis

2020 ◽  
Author(s):  
Yue Guan ◽  
Leiting Dong ◽  
Satya N. Atluri
Keyword(s):  
Numerical Integration ◽  
Sparse Matrices ◽  
Weak Form ◽  
Test Functions ◽  
The Finite Element Method ◽  
Element Free Galerkin ◽  
Piezoelectric Effects ◽  
Numerical Fluxes ◽  
Element Free ◽  
Methods Numerical

Abstract A meshless Fragile Points Method (FPM) is presented for analyzing 2D flexoelectric problems. Local, simple, polynomial and discontinuous trial and test functions are generated with the help of a local meshless differential quadrature approximation of the first three derivatives. Interior Penalty Numerical Fluxes are employed to ensure the consistency of the method. Based on a Galerkin weak-form formulation, the present FPM leads to symmetric and sparse matrices, and avoids the difficulties of numerical integration in the previous meshfree methods. Numerical examples including isotropic and anisotropic materials with flexoelectric and piezoelectric effects are provided as validations. The present method is much simpler than the Finite Element Method, or the Element-Free Galerkin (EFG) and Meshless Local Petrov-Galerkin (MLPG) methods, and the numerical integration of the weak form is trivially simple.

Multiscale Element–Free Galerkin Method with Penalty for 2D Burgers’ Equation

2013 ◽  
Vol 62 (3) ◽  
Author(s):  
Siaw Ching Liew ◽  
Su Hoe Yeak
Keyword(s):  
Meshless Method ◽  
Burgers Equation ◽  
Basis Functions ◽  
Polynomial Basis ◽  
The Finite Element Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Kronecker Delta ◽  
Local Enrichment ◽  
Element Free

In this paper, a new numerical method which is based on the coupling between multiscale method and meshless method with penalty is developed for 2D Burgers’ equation. The advantage of meshless method over the finite element method (FEM) is that remeshing process is not required. This is because the meshless method approximation is constructed entirely in terms of a set of nodes. Since the moving least squares (MLS) shape function does not satisfy the Kronecker delta property, so penalty method is adopted to enforce the essential boundary conditions in this paper. In order to obtain the fine scale approximation, the local enrichment basis is applied. The local enrichment basis may adopt the polynomial basis functions or any other analytical basis functions. Here, the polynomial basis functions are chosen as local enrichment basis. This multiscale meshless method with penalty will provide a more accurate result especially in the critical region which requires higher accuracy. It is believed that this proposed method is an attractive approach for solving more general problems which involve large deformation.

Estimation of the Crack Behaviour in the Compressive Layer of the Alumina-Zirconia Ceramic Laminate

2014 ◽  
Vol 627 ◽  
pp. 41-44
Author(s):  
Luboš Náhlík ◽  
Bohuslav Máša ◽  
Pavel Hutař
Keyword(s):  
Crack Propagation ◽  
Direct Method ◽  
Zirconia Ceramic ◽  
Finite Element Models ◽  
Linear Elastic ◽  
Dimensional Finite Element ◽  
Density Factor ◽  
Elastic Fracture ◽  
Energy Density Factor ◽  
Good Agreement

This paper deals with a description of the crack behaviour in the layered alumina-zirconia ceramic laminate. The main aim is to investigate the crack behaviour in the compressive layer. The crack propagation was investigated on the basis of linear elastic fracture mechanics. Two dimensional finite element models were developed in order to obtain a stress distribution around the crack tip. The stress intensity factors were computed numerically employing the direct method. The change in the crack propagation direction was estimated using criterion based on the strain energy density factor. Sharp crack deflection in the compressive layer was predicted by mentioned approach. The determined crack behaviour is qualitatively in a good agreement with experimental observations.

scholarly journals Prediction of Chloride Diffusion in Concrete Structure Using Meshless Methods

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Ling Yao ◽  
Xiaolu Li ◽  
Ling Zhang ◽  
Lingling Zhang
Keyword(s):  
Concrete Structure ◽  
Weighted Least Squares ◽  
Meshless Methods ◽  
Chloride Diffusion ◽  
Chloride Ingress ◽  
Rc Structures ◽  
Numerical Examples ◽  
Element Free Galerkin ◽  
Numerical Simulation Methods ◽  
Element Free

Degradation of RC structures due to chloride penetration followed by reinforcement corrosion is a serious problem in civil engineering. The numerical simulation methods at present mainly involve finite element methods (FEM), which are based on mesh generation. In this study, element-free Galerkin (EFG) and meshless weighted least squares (MWLS) methods are used to solve the problem of simulation of chloride diffusion in concrete. The range of a scaling parameter is presented using numerical examples based on meshless methods. One- and two-dimensional numerical examples validated the effectiveness and accuracy of the two meshless methods by comparing results obtained by MWLS with results computed by EFG and FEM and results calculated by an analytical method. A good agreement is obtained among MWLS and EFG numerical simulations and the experimental data obtained from an existing marine concrete structure. These results indicate that MWLS and EFG are reliable meshless methods that can be used for the prediction of chloride ingress in concrete structures.

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