Three-dimensional fracture analysis in transversely isotropic solids

Sáez, Andrés; Ariza, Manuel R. Gómez; Domínguez, José Ferreirós

doi:10.1016/s0955-7997(98)80003-9

Cited by 36 publications

(23 citation statements)

References 15 publications

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“…where the coefficientsN n ijk are independent of p. Substitution of equations (4.7) and (3.11) into equation (4.5), after the term-by-term integration, leads to 10) which is identical to equation (4.9) when p 4 = p 1 , p 5 = p 2 and p 6 = p 3 are taken. Similar to I n , the integral J n can be expressed by X (α) m as…”

Section: Stress Fundamental Solutionsmentioning

confidence: 99%

Unified analytical expressions of the three-dimensional fundamental solutions and their derivatives for linear elastic anisotropic materials

et al. 2016

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Novel unified analytical displacement and stress fundamental solutions as well as the higher order derivatives of the displacement fundamental solutions for three-dimensional, generally anisotropic and linear elastic materials are presented in this paper. Adequate integral expressions for the displacement and stress fundamental solutions as well as the higher order derivatives of the displacement fundamental solutions are evaluated analytically by using the Cauchy residue theorem. The resulting explicit displacement fundamental solutions and their first and second derivatives are recast into convenient analytical forms which are valid for non-degenerate, partially degenerate, fully degenerate and nearly degenerate cases. The correctness and the accuracy of the novel unified and closed-form three-dimensional anisotropic fundamental solutions are verified by using some available analytical expressions for both transversely isotropic (non-degenerate or partially degenerate) and isotropic (fully degenerate) linear elastic materials.

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Section: Stress Fundamental Solutionsmentioning

confidence: 99%

Unified analytical expressions of the three-dimensional fundamental solutions and their derivatives for linear elastic anisotropic materials

et al. 2016

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“…In the specific case of transversely isotropic materials the expressions deduced by Pan and Chou [17] are usually used in BEM codes [18,19]. Loloi [20] and Ariza and Domínguez [23] presented the expressions of the strongly singular and hypersingular kernel, respectively, obtained from Pan and Chou's [17] solution.…”

Section: Introductionmentioning

confidence: 99%

Recent developments in the evaluation of the 3D fundamental solution and its derivatives for transversely isotropic elastic materials

Mantič

Távara

Ortiz

et al. 2012

EJBE

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Abstract.Explicit closed-form real-variable expressions of a fundamental solution and its derivatives for three-dimensional problems in transversely linear elastic isotropic solids are presented. The expressions of the fundamental solution in displacements U ik and its derivatives, originated by a unit point force, are valid for any combination of material properties and for any orientation of the radius vector between the source and field points. An expression of U ik in terms of the Stroh eigenvalues on the oblique plane normal to the radius vector is used as starting point. Working from this expression of U ik , a new approach (based on the application of the rotational symmetry of the material) for deducing the first and second order derivative kernels, U ik,j and U ik,jℓ respectively, has been developed. The expressions of the fundamental solution and its derivatives do not suffer from the difficulties of some previous expressions, obtained by other authors in different ways, with complex valued functions appearing for some combinations of material parameters and/or with division by zero for the radius vector at the rotational symmetry axis. The expressions of U ik , U ik,j and U ik,jℓ are presented in a form suitable for an efficient computational implementation in BEM codes.

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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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Three-dimensional fracture analysis in transversely isotropic solids

Cited by 36 publications

References 15 publications

Unified analytical expressions of the three-dimensional fundamental solutions and their derivatives for linear elastic anisotropic materials

Unified analytical expressions of the three-dimensional fundamental solutions and their derivatives for linear elastic anisotropic materials

Recent developments in the evaluation of the 3D fundamental solution and its derivatives for transversely isotropic elastic materials

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

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