A non‐hypersingular time‐domain BIEM for 3‐D transient elastodynamic crack analysis

Zhang, Ch.; Groß, Dietmar

doi:10.1002/nme.1620361709

Cited by 41 publications

(16 citation statements)

References 29 publications

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Section: Time-domain Bem Formulationmentioning

confidence: 99%

“…We employ the BIE proposed in [15] and based on an alternative integral identity of linear elastodynamics. This BIE has been successfully applied to dynamic analysis of stationary, [15], and propagating cracks, [17], in finite or infinite domains. In contrast to the traction BIE, which is derived from the Betti-Rayleigh reciprocal theorem, [14], this BIE is non-hypersingular since all integrals exist at least in the Cauchy principal value sense.…”

Section: Time-domain Bem Formulationmentioning

confidence: 99%

“…Then a distinct set of boundary integral equations is obtained by applying the traction equation (15) for collocation points along the crack face C þ C and displacement equations (16) and (17) along the external boundary C 1 s þ C 1 r þ C 1 u of domain 1 and C 2 s þ C 2 r þ C 2 u of domain 2, respectively. Within each time step, the displacements are approximated by linear time-interpolating functions and the tractions are piecewise constant.…”

Section: Numerical Solution Proceduresmentioning

confidence: 99%

“…Time-domain boundary element method (BEM), which has been successfully applied in homogeneous medium, [12][13][14][15][16][17][18], is introduced into the bi-material system. Two kinds of time-domain BEM are applied: the time-domain displacement BEM, [14], and the non-hypersingular traction BEM, [15,16].…”

Section: Introductionmentioning

confidence: 99%

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Dynamic interaction between a sub-interface crack and the interface in a bi-material: time-domain BEM analysis

Lei

Wang

Groß

2003

Archive of Applied Mechanics (Ingenieur Archiv)

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Transient response of a sub-interface crack in a bi-material is studied with emphasis on the dynamic interaction between the crack and the interface, by combining the traditional time-domain displacement boundary element method (BEM) and the non-hypersingular traction BEM. Computations are performed for an unbounded bi-material with a crack subjected to impact tensile loading on its faces or incident impact waves and a bounded rectangular bi-material plate under remote impact tensile loading. Numerical results of the dynamic stress intensity factors (DSIFs) and dynamic interface tractions are presented for various material combinations and crack locations. It is shown that pronounced increases in DSIFs and the interface tractions may be caused in some cases because of the dynamic interaction between the crack and the interface. IntroductionWith the increased use of composite materials in engineering applications in recent decades, understanding the mechanism of dynamic fracture in multiphase materials becomes more and more important. Many problems of crack-interface interaction need deeper exploration.Most publications concerning dynamic fracture in multiphase materials are focused on the dynamic behavior of interfacial cracks [1-9]. However, it is known that flaws can appear not only on the interface but also in the component materials. Therefore, it is equally important to study the dynamic response of sub-interface cracks with consideration of the crack-interface interaction. Up to now, only few publications have considered this problem: among them, paper [10] studied the dynamic response of a layered composite under normal and shear impact in which the crack is parallel to the interface, and Ref.[11] studied the situation of a crack normal to the interface.The present paper studies the transient response of an arbitrary sub-interface crack in an unbounded or bounded bi-material under in-plane impact loading and discusses the effects of the material mismatch and crack location on the dynamic stress intensity factors (DSIFs) and interface tractions. Time-domain boundary element method (BEM), which has been successfully applied in homogeneous medium, [12][13][14][15][16][17][18], is introduced into the bi-material system.

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Section: Time-domain Bem Formulationmentioning

confidence: 99%

Section: Time-domain Bem Formulationmentioning

confidence: 99%

Section: Numerical Solution Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic interaction between a sub-interface crack and the interface in a bi-material: time-domain BEM analysis

Lei

Wang

Groß

2003

Archive of Applied Mechanics (Ingenieur Archiv)

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“…Most of these studies first reduced the high order singularities to integrable ones, and then solved the modified BIE's numerically. A simple and straightforward derivation of non-hypersingular BIEs for elastodynamic crack analysis was recently proposed by Zhang, Achenbach and Gross [13][14][15][16], where a two-state conservation integral of elastodynamics is used and the unknown quantities are the crack opening displacements and their derivatives. The dynamic crack problems of 2D and 3D infinite bodies have been solved by them in both the time domain and the frequency domain.…”

Section: Introductionmentioning

confidence: 99%

The mixed-type integral equations for transient elastodynamic plane crack problems

1996

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Abstract. In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems. I n t r o d u c t i o nIn fracture dynamics, the impact or transient loading problems possess high value of practice and theory. But due to mathematical difficulties, the solution of problems in classical elastodynamics remains an extremely complicated and difficult task. Only limited solutions in a closed form have been obtained for infinite domain problems. To obtain solutions for finite and irregular domains, there is a clear need for developing powerful theory and effective numerical techniques which can model arbitrary time-dependent loads and geometry.In special transient crack problems, the Griffith crack problem may be the most basic one. This problem was firstly considered by Sih and Chen [1 ]. They applied the Laplace-Fourier integral transforms and obtained a system of dual integral equations. In 1980's the method was further applied to some other special problems [2][3][4][5]. In general ones, the pure numerical methods, finite difference method (FDM) and finite element method (FEM) have been applied with some success to solve dynamic problems of cracks. But some difficulties in using FDM and FEM for fracture dynamics have been pointed out [6]. The boundary integral equation method (BIEM) provides an efficient numerical approach towards crack analysis. However the conventional displacement BIE formulation gives rise to degenerate integral equations for crack problems and is not suitable for numerical solutions. For dynamic crack problem, the ordinary BIEM was firstly used by Fan and Hahn [7], Sladek and Sladek [8], Chirno and Dominguez [9], where the domain has to be divided into subdomains by means of a cut along the crack. To circumvent the difficulties in using the ordinary integral equation method, several other approaches have been proposed; see for example, the papers by Cruse [10], Sladek and Sladek [11 ], Nishimura and Kobayashi [ 12]. Most of these studies first reduced the high order singularities to integrable ones, and then solved the modifi...

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A time-dependent formulation of dual boundary element method for 3D dynamic crack problems

Wen

Aliabadi

Young³

1999

Int. J. Numer. Meth. Engng.

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SUMMARYIn this paper, the dual boundary element method in time domain is developed for three-dimensional dynamic crack problems. The boundary integral equations for displacement and traction in time domain are presented. By using the displacement equation and traction equation on crack surfaces, the discontinuity displacement on the crack can be determined. The integral equations are solved numerically by a time-stepping technique with quadratic boundary elements. The dynamic stress intensity factors are calculated from the crack opening displacement. Several examples are presented to demonstrate the accuracy of this method.

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A non‐hypersingular time‐domain BIEM for 3‐D transient elastodynamic crack analysis

Cited by 41 publications

References 29 publications

Dynamic interaction between a sub-interface crack and the interface in a bi-material: time-domain BEM analysis

Dynamic interaction between a sub-interface crack and the interface in a bi-material: time-domain BEM analysis

The mixed-type integral equations for transient elastodynamic plane crack problems

A time-dependent formulation of dual boundary element method for 3D dynamic crack problems

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