Extended displacement discontinuity Green's functions for three-dimensional transversely isotropic magneto-electro-elastic media and applications

Zhao, Minghao; Fan, CuiYing; Liu, Tong; Yang, Feng

doi:10.1016/j.enganabound.2006.11.002

Cited by 31 publications

(29 citation statements)

References 23 publications

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“…The extended Crouch fundamental solution for constant elements in magnetoelectroelastic media was presented by Zhao et al [21]. To improve the accuracy of the numerical solution, the parabolic element was developed in the DDM for purely elastic media by Scavia [28].…”

Section: The Crouch Fundamental Solutions For Parabolic Elementsmentioning

confidence: 99%

“…Using Dual BEM, the behavior of cracked linear magnetoelectroelastic solids was analyzed by García-Sánchez et al [18]. Displacement discontinuity method (DDM) proposed by Crouch [19] is an effective method for analysis of cracks in elastic materials and has been extended to problems of piezoelectric and magnetoelectroelastic media [20,21]. Different electric and magnetic boundary conditions on crack faces were easily and naturally embedded in the extended DDM [7].…”

Section: Introductionmentioning

confidence: 99%

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Numerical method of crack analysis in 2D finite magnetoelectroelastic media

Zhao

Fan

2009

Comput Mech

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The present paper extends the hybrid extended displacement discontinuity fundamental solution method (HEDD-FSM) (Eng Anal Bound Elem 33:592-600, 2009) to analysis of cracks in 2D finite magnetoelectroelastic media. The solution of the crack is expressed approximately by a linear combination of fundamental solutions of the governing equations, which includes the extended point force fundamental solutions with sources placed at chosen points outside the domain of the problem under consideration, and the extended Crouch fundamental solutions with extended displacement discontinuities placed on the crack. The coefficients of the fundamental solutions are determined by letting the approximated solution satisfy the prescribed boundary conditions on the boundary of the domain and on the crack face. The Crouch fundamental solution for a parabolic element at the crack tip is derived to model the square root variations of near tip fields. The extended stress intensity factors are calculated under different electric and magnetic boundary conditions.

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Section: The Crouch Fundamental Solutions For Parabolic Elementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical method of crack analysis in 2D finite magnetoelectroelastic media

Zhao

Fan

2009

Comput Mech

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“…At the same time, due to the inherent characteristics of its formulation, BEM provides very accurate results for problems containing strong geometrical discontinuities. Fracture mechanical analysis of three-dimensional transversely isotropic materials using BEM has been reported in [Sáez et al 1997;Ariza and Dominguez 2004a;2004b], which modeled static and dynamic crack problems, [Zhao et al 2007], which derived the displacement discontinuity boundary integral equation, and more recently in [Chen et al 2009], which studied the stress intensity factors of a central square crack in a transversely isotropic cuboid with arbitrary material orientations. To our knowledge, there is no published material about three-dimensional BEM modeling of interface cracks in dissimilar transversely isotropic bimaterials.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional BEM analysis to assess delamination cracks between two transversely isotropic materials

Larrosa¹,

Ortiz

Cisilino

2011

J. Mech. Mater. Struct.

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Beyond the inherent attribute of reducing the dimensionality of the problem, the attraction of the boundary element method (BEM) for dealing with fracture mechanic problems is its accuracy in solving strong geometrical discontinuities. Within this context, a three-dimensional implementation of the energy domain integral (EDI) for the analysis of interface cracks in transversely isotropic bimaterials is presented in this paper. The EDI allows extending the two-dimensional J -integral to three dimensions by means of a domain representation naturally compatible with the BEM, in which the required stresses, strains, and derivatives of displacements are evaluated using their appropriate boundary integral equations. To this end, the BEM implementation uses a set of recently introduced fundamental solutions for transversely isotropic materials. Several examples are solved in order to demonstrate the efficiency and accuracy of the implementation for solving straight and curved crack-front problems.

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“…Using the integral equation method in Zhao et al [7], the Green functions for unit-point discontinuities are obtained. For simplicity, the final expressions of the Green functions are omitted.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the subsequent displacement discontinuity boundary integral equation and boundary element method are more efficient in studying crack problems, as they grasp the basic characteristic of crack problems; specifically, fields are discontinuous across crack faces. The displacement discontinuity method was first proposed by Crouch [5] to study two-dimensional crack problems, and was then extended to three-dimensional elastic media, piezoelectric media, and magnetoelectroelastic media [6][7][8][9], where the electric and magnetic potential discontinuities were introduced across crack faces. Based on previous work, this paper develops the temperature and displacement discontinuity boundary integral equation and boundary element method for which the temperature distribution across the crack faces is assumed discontinuous.…”

mentioning

confidence: 99%

Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media

Zhao¹,

Dang²,

Li³

et al. 2017

Int. J. CMEM

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For the analysis of cracks in three-dimensional isotropic thermoelastic media, a temperature and displacement discontinuity boundary element method is developed. The Green functions for unit-point temperature and displacement discontinuities are derived, and the temperature and displacement discontinuity boundary integral equations are obtained for an arbitrarily shaped planar crack. Our boundary element method is based on the Green functions for a triangular element. As an application, elliptical cracks are analyzed to validate the developed method. The influence of various thermal boundary conditions is studied. Keywords: boundary element method, boundary integral equation method, displacement and temperature discontinuity, Green function, isotropic thermoelastic medium, planar crack, stress intensity factor, thermal boundary condition, triangular element. INTRODUCTIONMuch research has been conducted in the analysis of cracks in thermoelastic materials using analytical or numerical methods [1][2][3][4]. Because solving complicated practical problems analytically is difficult, numerical methods are needed. Among the various numerical methods, the boundary element method is very convenient and efficient in such analyses, and many studies have adopted this method to analyze crack problems in thermoelastic media [2][3][4]. Furthermore, the subsequent displacement discontinuity boundary integral equation and boundary element method are more efficient in studying crack problems, as they grasp the basic characteristic of crack problems; specifically, fields are discontinuous across crack faces. The displacement discontinuity method was first proposed by Crouch [5] to study two-dimensional crack problems, and was then extended to three-dimensional elastic media, piezoelectric media, and magnetoelectroelastic media [6][7][8][9], where the electric and magnetic potential discontinuities were introduced across crack faces. Based on previous work, this paper develops the temperature and displacement discontinuity boundary integral equation and boundary element method for which the temperature distribution across the crack faces is assumed discontinuous. The Green functions for unit-point temperature and displacement discontinuities are derived, and the temperature and displacement discontinuity boundary integral equations are obtained for an arbitrarily shaped planar crack. The singular fields ahead of the crack front are discussed, and the stress intensity factors are obtained. For numerical simulations, the Green functions for a triangular element are obtained, and an elliptical crack is analyzed to validate the correctness of the analytical solution and the proposed numerical method. The influence of the temperature and different thermal conditions are also discussed.

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Extended displacement discontinuity Green's functions for three-dimensional transversely isotropic magneto-electro-elastic media and applications

Cited by 31 publications

References 23 publications

Numerical method of crack analysis in 2D finite magnetoelectroelastic media

Numerical method of crack analysis in 2D finite magnetoelectroelastic media

Three-dimensional BEM analysis to assess delamination cracks between two transversely isotropic materials

Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media

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