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A fractional differential constitutive model for dynamic stress intensity factors of an anti-plane crack in viscoelastic materials

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Acta Mechanica Sinica 2014年第3期30卷 403-409页

作者： Run-Tao Zhan Zhao-Xia Li Lei Wang Department of Engineering Mechanics Southeast UniversityJiangsu Key Laboratory of Engineering Mechanics School of Civil Engineering Southeast University

Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.

关键词： Dynamic fracture stress intensity factors Fractional differentiation - Anti-plane fracture Viscoelasticmaterial Wiener-Hopf

Extraction of stress intensity factors by Using the P-Version Finite Element Method and Contour Integral Method

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Acta Mechanica Solida Sinica 2020年第6期33卷 836-850页

作者： Jianming Zhang Jun Chen Liang Wu Department of Engineering Mechanics Kunming University of Science and TechnologyKunming 650500China Department of Water Resources and Hydropower Engineering Kunming University of Science and TechnologyKunming 650500China

The stress intensity factors(SIFs)for two-dimensional cracks are extracted using the p-version finite element method(P-FEM)and the contour integral *** numerical experiments,e.g.,crack initiating from the edge of a circular hole under an unidirectional uniform tension and two equal-length,unequal-length hole-edge cracks,respectively,at a rectangular plate,an inclined centered crack under uniaxial tension at a square plate and a pipeline crack model,are used to demonstrate the accuracy and effectiveness of the *** are presented for the effects of various crack lengths and length-width *** results are analyzed and compared with reference solutions and results obtained by the Voronoi cell finite element method,boundary element method,high-order extended finite element method(high-order XFEM)and commercial finite element software ABAQUS in the available *** results are in good agreement with the benchmark problems and show faster convergence rate,higher accuracy and better numerical stability.

关键词： Fracture mechanics stress intensity factors P-version finite element method Contour integral method

METHOD TO CALCULATE BENDING CENTER AND stress intensity factors OF CRACKED CYLINDER UNDER SAINT-VENANT BENDING

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Applied Mathematics and Mechanics(English Edition) 2001年第1期22卷 79-88页

作者： TANG Pen-ji(汤任基) TANG Xin-yan(汤昕燕) Department of Engineering Mechanics Shanghai Jiaotong University Shanghai 200030 P R China Agricultural Engineering College Nanjing Agricultural University Nanjing 210032 P R China

Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross-section is not thin-walled, but of small torsion rigidity is proposed. Some numerical examples are given.

关键词： cracked cylinger Saint-Venant bending bending center stress intensity factors integral equation method

COMPUTATION OF stress intensity factors BY THE SUB-REGION MIXED FINITE ELEMENT METHOD OF LINES

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Acta Mechanica Solida Sinica 2007年第2期20卷 149-162页

作者： Yuan Si Xu Yongjun WILLIAMS F W Department of Civil Engineering Tsinghua University Beijing 100084 China Institute of Mechanics Chinese Academy of Sciences Beijing 100080 China Structural Engineering Division Cardiff University Cardiff CF2 3TB UK

Based on the sub-region generalized variationM principle, a sub-region mixed version of the newly-developed semi-analytical ＇finite element method of lines＇（FEMOL） is proposed in this paper for accurate and efficient computation of stress intensity factors （SIFs） of two-dimensional notches/cracks. The circular regions surrounding notch/crack tips are taken as the complementary energy region in which a number of leading terms of singular solutions for stresses are used, with the sought SIFs being among the unknown coefficients. The rest of the arbitrary domain is taken as the potential energy region in which FEMOL is applied to obtain approximate displacements. A mixed system of ordinary differential equations （ODEs） and algebraic equations is derived via the sub-region generalized variational principle. A singularity removal technique that eliminates the stress parameters from the mixed equation system eventually yields a standard FEMOL ODE system, the solution of which is no longer singular and is simply and efficiently obtained using a standard general-purpose ODE solver. A number of numerical examples, including bi-material notches/cracks in anti-plane and plane elasticity, are given to show the generally excellent performance of the proposed method.

关键词： stress intensity factors finite element method of lines sub-region generalized variational principle ordinary differential equation solver

AN INVESTIGATION ON stress intensity factors OF INTERFACE CRACK FOR THREE TYPES OF SPECIMENS

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Acta Mechanica Solida Sinica 2000年第1期13卷 42-49页

作者： Shi Junping Liu Xiehui Mo Xiaoyi Chen Yiheng Department of Engineering Mechanics Xi'an Universiry of TechnologyXi'an 710048China School of Civil Eingineering and Mechanics Xi'an Jiaotong UniversityXi'an 710049China

The problems of finite bimaterial plates, hearing uniform tension, compact: tension and three point bending, are studied by using the eigenfunction expansion variation method (EEVM). And interfacial stress intensity factors (SIFs) are determined. The SIFs varying with shear modulus mu and Poisson's ratios nu of both materials are discussed.

关键词： bimaterial eigenfunction expansion interface crack stress intensity factors

stress intensity factors FOR A PIEZOELECTRIC PLATE WITH A SEMI-PERMEABLE CRACK UNDER UNIFORM THERMAL AND ELECTRIC LOADS

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STRESS INTENSITY FACTORS FOR A PIEZOELECTRIC PLATE WITH A SE...

Numerical Comparison Research on the Solution of stress intensity factors of Multiple Crack Problems

2013全国压电和声波理论及器件技术研讨会

作者： Shi-Chao XING Cun-Fa GAO State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics & Astronautics

In this paper we analyze the two-dimensional piezoelectric material with a center crack by means of complex variable *** material is subjected to uniform heat flow qand electric displacement Dat infinity,and the heat flow on the crack isλq,the electric displacement on the crack isλD,*** complex potentials of temperature field and the electroelastic fields are obtained,and finally the solutions for the intensity factors are presented in *** results are given to discuss the effects of crack surface boundary conditions on the intensity factors of *** is found that when the crack length is fixed,the vector of field intensity factors is linearly changed as the insulation coefficientλ andλ.

关键词： Partially insulated Piezoelectric materials Hilbert problem stress intensity factors

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Advances in Pure Mathematics 2020年第12期10卷 706-727页

作者： Guo Zhao College of Architecture Engineering and Planning Jiujiang University Jiujiang China

A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) boundary integral equations in this paper. The eigen COD is defined as a crack in an infinite domain under fictitious traction acting on the crack surface. Respect to the computational accuracies and efficiencies, the multiple crack problems in finite and infinite plates are solved and compared numerically using three different kinds of boundary integral equations (BIEs): 1) the dual BIEs require crack surface discretization;2) the BIEs with numerical Green’s functions (NGF) without crack surface discretization, but have to solve a complementary matrix;3) the eigen crack opening displacement (COD) BIEs in the present paper. With the concept of eigen COD, the multiple crack problems can be solved by using a conventional displacement discontinuity boundary integral equation in an iterative fashion with a small size of system matrix as that in the NGF approach, but without troubles to determine the complementary matrix. Solution of the stress intensity factors of multiple crack problems is solved and compared in some numerical examples using the above three computational algorithms. Numerical results clearly demonstrate the numerical models of eigen COD BIEs have much higher efficiency, providing a newly numerical technique for multiple crack problems. Not only the accuracy and efficiency of computation can be guaranteed, but also the overall properties and local details can be obtained. In conclusion, the numerical models of eigen COD BIEs realize the simulations for multiple crack problems with large quantity of cracks.

关键词： Multiple Crack Problems Boundary Integral Equations Eigen Crack Opening Displacements Eshelby Matrix stress intensity factors

An Element-free Galerkin Scaled Boundary Method for stress intensity factors and Higher Order Terms

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An Element-free Galerkin Scaled Boundary Method for Stress I...

SCATTERING OF SH-WAVE BY CRACKS ORIGINATING AT AN ELLIPTIC HOLE AND DYNAMIC stress intensity FACTOR

第16届全国疲劳与断裂学术会议

作者：何宜谦杨海天 Andrew J.Deeks 大连理工大学工程力学系

This study applies a new Element-free Galerkin scaled boundary method(EFG-SBM) to determine the stress intensity factor(SIFs) and higher order terms. The SBM is an accurate semi-analytical method originally developed ... 详细信息

关键词： Scaled boundary method Element-free Galerkin method stress intensity factors Higher order terms

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Applied Mathematics and Mechanics(English Edition) 2004年第9期25卷 1047-1056页

作者：刘殿魁陈志刚 School of Civil Engineering Harbin Engineering University Department of Civil Engineering Jinan University

The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.

关键词： Fracture mechanics Green's function Integral equations Scattering stress intensity factors Surface waves Crack tip Elastic half space Elliptic hole Griffith linear crack SH wave