Computational fracture mechanics: Research and application

Liebowitz, Harold; Sandhu, Jeet; Lee, J.D.; Menandro, Fernando César Meira

doi:10.1016/0013-7944(94)e0051-h

Cited by 31 publications

(18 citation statements)

References 26 publications

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“…This crack interaction phenomenon was experimentally observed by Sinha et al [56]. Numerical simulations were also reported in the literature (Swenson [57], Liebowitz [29], and Marzougui [19]). To verify the e ectiveness of current implementation of the fracture model, the dynamic propagation processes of two interacting cracks is simulated.…”

Section: Validation Of the Pseudo 3d Fracture Modelsmentioning

confidence: 58%

Development of the DYNA3D simulation code with automated fracture procedure for brick elements

Tabiei

Jin

2003

Numerical Meth Engineering

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SUMMARYNumerical simulation of cracked structures is an important aspect in structural safety assessment. In recent years, there has been an increasing rate of development of numerical codes for modelling fracture procedure. The subject of this investigation is implementing automated fracture models in the DYNA3D non-linear explicit ÿnite element code to simulate pseudo 3D crack growth procedure. The implemented models have the capabilities of simulating automatic crack propagation without user intervention. The implementation is carried on solid elements. The methodology of implementing fracture models is described. An element deletion-and-replacement remeshing procedure is proposed for updating the explicit geometric description of evolving cracks. Fracture parameters such as stress intensity factors, energy release rates and crack tip opening angle are evaluated. The maximum circumferential stress criterion is used to predict the direction of crack advancement. Seven crack problems are presented to verify the e ectiveness of the methodology. Mesh sensitivity and loading rate e ects are studied in the validation of the presented procedure.

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Section: Validation Of the Pseudo 3d Fracture Modelsmentioning

confidence: 58%

Development of the DYNA3D simulation code with automated fracture procedure for brick elements

Tabiei

Jin

2003

Numerical Meth Engineering

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“…Therefore, the use of finer elements cannot improve the situation either. In order to improve the convergence rate of the FE solution, various attempts have been made to include the required crack tip singularity in the element formulation, as has been extensively reviewed by Gallagher [2], Fawkes et al [3], Owen and Fawkes [4], Liebowitz and Moyer [5], and Liebowitz et al [6].…”

Section: Introductionmentioning

confidence: 99%

XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi‐materials

Liu

Xiao

Karihaloo

2004

Numerical Meth Engineering

194

166

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SUMMARYThe extended finite element method (XFEM) is improved to directly evaluate mixed mode stress intensity factors (SIFs) without extra post-processing, for homogeneous materials as well as for bimaterials. This is achieved by enriching the finite element (FE) approximation of the nodes surrounding the crack tip with not only the first term but also the higher order terms of the crack tip asymptotic field using a partition of unity method (PUM). The crack faces behind the tip(s) are modelled independently of the mesh by displacement jump functions. The additional coefficients corresponding to the enrichments at the nodes of the elements surrounding the crack tip are forced to be equal by a penalty function method, thus ensuring that the displacement approximations reduce to the actual asymptotic fields adjacent to the crack tip. The numerical results so obtained are in excellent agreement with analytical and numerical results available in the literature.

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“…For the application of energy approach to dynamic fracture problems, Nakamura et al [3] developed the following 2-D integral expression for dynamic energy release rate of a plane crack in a linear elastic body advancing in the x 1 (1) direction (normal to the crack tip): (2) where U is the strain energy density, T is the kinetic energy density, σ ij are the components of stress, u i are the components of displacements, ρ is the mass density of the material, n j are the components of the unit normal vector to a contour Γ 0 around the crack tip which begins on one crack face and ends on the opposite face, and A 0 is the area enclosed by Γ 0 , another contour Γ around the crack tip but closer, and a portion of crack faces between the end points of the contours. The contours and area are shown in figure (1).…”

Section: Integral Expression For Dynamic Energy Release Rate In Lineamentioning

confidence: 99%

“…Therefore, the advancement of dynamic fracture mechanics relies heavily on parallel advances in computational methods for dynamic fracture simulation [1]. A detailed review of the impact of computational technology on furthering the understanding of fundamental fracture phenomena can be found in [2].…”

Section: Introductionmentioning

confidence: 99%