Experimental and numerical comparisons between finite element method, element-free Galerkin method, and extended finite element method predicted stress intensity factor and energy release rate of cortical bone considering anisotropic bone modelling

2019 ◽  
Vol 233 (8) ◽  
pp. 823-838 ◽  
Author(s):  
Ajay Kumar ◽  
Pankaj Shitole ◽  
Rajesh Ghosh ◽  
Rajeev Kumar ◽  
Arpan Gupta
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Galerkin Method ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free ◽  
Element Method

Stress intensity factor and energy release rate are important parameters to understand the fracture behaviour of bone. The objective of this study is to predict stress intensity factor and energy release rate using finite element method, element-free Galerkin method, and extended finite element method and compare these results with the experimentally determined values. For experimental purpose, 20 longitudinally and transversely fractured single-edge notched bend specimens were prepared and tested according to ASTM standard. All specimens were tested using the universal testing machine. For numerical simulations (finite element method, element-free Galerkin method, and extended finite element method), two-dimensional model of cortical bone was developed by assuming plane strain condition. Material properties of the cortical bone were considered as anisotropic and homogeneous. The values obtained through finite element method, element-free Galerkin method, and extended finite element method are well corroborated to experimentally determined values and earlier published data. However, element-free Galerkin method and extended finite element method predict more accurate results as compared to finite element method. In the case of the transversely fractured specimen, the values of stress intensity factor and energy release rate were found to be higher as compared to the longitudinally fractured specimen, which shows consistency with earlier published data. This study also indicates element-free Galerkin method and extended finite element method predicted stress intensity factor and energy release rate results are more close to experimental results as compared to finite element method, and therefore, these methods can be used in the different field of biomechanics, particularly to predict bone fracture.

scholarly journals An element-free Galerkin method for electromechanical coupled analysis in piezoelectric materials with cracks

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769373
Author(s):  
Xiao Lin Li ◽  
Li Ming Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Piezoelectric Materials ◽  
New Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free ◽  
Electromechanical Coupled ◽  
Element Method

We present an element-free Galerkin method for electromechanical coupled fracture analysis in piezoelectric materials. Singularity terms were introduced into the approximation function of the new method to describe the displacement and electric fields near the crack. The new method requires a smaller domain to describe the crack-tip singular field compared with the finite element method. Then, we computed the J-integrals of piezoelectric materials and investigated the effects of crack length on the computational precision. Numerical examples were used to highlight the accuracy of the new method compared with the analytical solutions and finite element method.

Element-Free Galerkin Method of Cold Forging Steel Ball

2014 ◽  
Vol 1004-1005 ◽  
pp. 1046-1049
Author(s):  
Ye Yuan ◽  
Hong Bin Liu ◽  
Hai Tao Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Steel Ball ◽  
Cold Forging ◽  
Element Free Galerkin Method ◽  
Forming Process ◽  
Element Free Galerkin ◽  
Element Free ◽  
Element Method

The fundamental principle of three dimensional Element-free Galerkin has been briefly investigated in this paper, and built forming mode of steel ball cold forging, Element-free Galerkin method successfully applied to the simulation analysis of steel ball cold forging forming process in the LS-DYNA simulation software. In comparison to Finite Element Method and experiment data, Proved Element-free Galerkin method was feasible in metal plastic forming process, and in the large deformation simulation was more accurate than the finite element method, Element-free Galerkin method has more obvious advantages after altering the impact factors.

Application of Extended Finite Element Method (XFEM) to Stress Intensity Factor Calculations

2015 ◽  
Author(s):  
Do-Jun Shim ◽  
Mohammed Uddin ◽  
Sureshkumar Kalyanam ◽  
Frederick Brust ◽  
Bruce Young
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Partition Of Unity ◽  
Extended Finite Element ◽  
Element Method

The extended finite element method (XFEM) is an extension of the conventional finite element method based on the concept of partition of unity. In this method, the presence of a crack is ensured by the special enriched functions in conjunction with additional degrees of freedom. This approach also removes the requirement for explicitly defining the crack front or specifying the virtual crack extension direction when evaluating the contour integral. In this paper, stress intensity factors (SIF) for various crack types in plates and pipes were calculated using the XFEM embedded in ABAQUS. These results were compared against handbook solutions, results from conventional finite element method, and results obtained from finite element alternating method (FEAM). Based on these results, applicability of the ABAQUS XFEM to stress intensity factor calculations was investigated. Discussions are provided on the advantages and limitations of the XFEM.

A Coupled Finite Element-Element Free Galerkin Method for Liquefiable Soil-Structure Interaction Analysis Under Earthquake Loading

2009 ◽  
Author(s):  
Xiaowei Tang ◽  
Ying Jie ◽  
Maotian Luan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Soil Structure ◽  
Soil Structure Interaction ◽  
Element Free Galerkin Method ◽  
Structure Interaction ◽  
Element Free Galerkin ◽  
Liquefiable Soil ◽  
Element Free

This study presents a numerical method for the seismic behavior assessment of liquefiable soil-structure interaction. In the method, the element-free Galerkin method (EFGM) is applied to simulate the behavior of the liquefiable sandy soil which will take place large permanent deformation under earthquake loading. The finite element method (FEM) is used to describe the behavior of the structure. Then, the EFGM and FEM are related by contact elements. The cyclic elasto-plastic constitutive model and updated Lagrangian large-deformation formulation are jointly adopted to establish the governing equations in order to take account for both physical and geometrical nonlinearities. The shape function is established by moving least squares method while hexahedral background cells are used. The essential boundary conditions are treated with the help of the penalty method. The coupled method can avoid the volumetric locking in the numerical computations using finite element method when non-uniform deformations happen. In order to assess the effectiveness and accuracy of the current procedure, numerical simulation of caisson-type quay wall subjected to earthquake motion is conducted.

Numerical Study of Stress Intensity Factor in Notched Specimens Using Extended Finite Element Method

2012 ◽  
Vol 166-169 ◽  
pp. 2995-2998
Author(s):  
Geng Chen ◽  
Tao Xu ◽  
Qiang Xu ◽  
Lin Bu
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Numerical Simulations ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Notched Specimens ◽  
Element Method

The principle of the structure of displacement function, the establishment of governing equations, level set method were briefly outlined in this paper. Numerical simulations on three dimensional single edge notched specimens with different crack length in tension were performed using Abaqus software based on extended finite element method (XFEM), the stress intensity factor at static crack front was analyzed and the simulated results were in good agreement with analytical solutions. Numerical simulations in the present paper indicated that the extended finite element method is very suitable to deal with nonlinear fracture problems.

Modal Stress Intensity Factor Using Extended Finite Element Method

2012 ◽  
Vol 232 ◽  
pp. 686-690 ◽  
Author(s):  
Benmessaoud Abdelkader ◽  
Badaoui Mohamed ◽  
Hachi Brahim El-Khalil ◽  
Nehar Camellia Khaira ◽  
Guesmi Mohamed
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Extended Finite Element Method ◽  
Computational Time ◽  
Extended Finite Element ◽  
Modal Stress ◽  
Element Method

The aim of this paper is the determination of the evolution of the modal stress intensity factor (MSIF) for a non-propagating crack subjected to dynamic loading using the extended finite element method (X-FEM). The main advantage of this method coupled with the modal analysis is its capability in modeling cracks independently of the mesh and in a reduced computational time compared to the finite element method coupled with dynamic iterative method. The proposed procedure is applied to a reference problem (cracked plate). The MSIFs obtained agree well with those found by indirect boundary element (IBEM), weight function and Newmark’s explicit methods.

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