Numerical studies in dynamic fracture mechanics

Atluri, S. N.; Nishioka, Toshihisa

doi:10.1007/bf00017971

Cited by 44 publications

(7 citation statements)

References 35 publications

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“…where E * is the e ective Young's modulus proposed by Cherapanov: (12) where t , n , and f are strains measured close to the crack front along the tangent, normal, and binormal to the crack front (surface). The dynamic fracture toughness is a function of the crack speed given by…”

Section: Physical Modelmentioning

confidence: 99%

“…The moving mesh technique was used by Atluri and Nishioka 12 (with the FEM), Koh, Lee and Haber 13 (Eulerian-Lagrangian description in conjunction with the FEM), Gallego and Dominguez 14 (BEM with a moving singular element), Koh et al, 15 (Eulerian-Lagrangian description in conjunction with the FEM). Modelling arbitrary curved crack growth seems to be di cult with this approach, since excessive mesh distortion will occur.…”

Section: -D Crack Growth Simulationsmentioning

confidence: 99%

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The Element Free Galerkin method for dynamic propagation of arbitrary 3-D cracks

Krysl

Belytschko

1999

Int. J. Numer. Meth. Engng.

238

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SUMMARYA technique for modelling of arbitrary three-dimensional dynamically propagating cracks in elastic bodies by the Element-Free Galerkin (EFG) method with explicit time integration is described. The meshless character of this approach expedites the description of the evolving discrete model; in contrast to the ÿnite element method no remeshing of the domain is required. The crack surface is deÿned by a set of triangular elements. Techniques for updating the surface description are reported. The paper concludes with several examples: a simulation of mixed-mode growth of a center crack, mode-I surface-breaking penny-shaped crack, penny-shaped crack growing under mixed-mode conditions in a cube, and a bar with centre through crack.

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Section: Physical Modelmentioning

confidence: 99%

Section: -D Crack Growth Simulationsmentioning

confidence: 99%

The Element Free Galerkin method for dynamic propagation of arbitrary 3-D cracks

Krysl

Belytschko

1999

Int. J. Numer. Meth. Engng.

238

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“…Due to the aforementioned difficulties, the finite element method has been mostly limited to two-dimensional problems with the crack confined to its original line. While early work focused on various node release techniques and on the development of special singular elements moving with the crack tip (Atluri and Nishioka, 1985), recent work has included the introduction of special adaptive h-p methods for hyperbolic systems (Safjan and Oden, 1993) and of Eulerian-Lagrangian formulations to better cope with the continuously changing geometry (Koh et al, 1988). To study the spontaneous out-of-plane motion of two-dimensional dynamically propagating cracks, Swenson and Ingraffea (1988) used remeshing and interactive graphics to control the mesh distortion, while, more recently, Xu and Needleman (1994) introduced a cohesive surface constitutive relation allowing for the creation of new free surfaces along a family of possible fracture directions.…”

Section: Introductionmentioning

confidence: 99%

A spectral method for three-dimensional elastodynamic fracture problems

Geubelle¹

1995

Journal of the Mechanics and Physics of Solids

200

209

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We present a numerical formulation for three-dimensional elastodynamic problems of fracture on planar cracks and faults. Stress and displacement components are given a spectral representation as finite Fourier series in space coordinates parallel to the fracture plane. The formulation is based on an exact representation, involving a convolution integral for each Fourier mode, of the elastodynamic relation existing between the time-dependent Fourier coefficients for the tractions acting on the fracture plane and for the resulting displacement discontinuities. A wide range of constitutive models can be used to relate the local value of the strength on the fracture plane with the displacement and velocity history. Efficiency of the code is achieved by using an explicit time integration scheme and by computing the conversion between the spatial and spectral distributions through a FFT algorithm. The method is particularly suited to implementation on massively parallel computers ; a CM-5 was used in this work. The stability and precision of the formulation are discussed for tensile (mode I) situations in a detailed modal analysis, and numerical results are compared with existing three-dimensional elastodynamic solutions. The adequacy of the method to investigate various three-dimensional dynamic fracture problems involving non-propagating and propagating tensile cracks is illustrated, including crack growth along a plane of heterogeneous fracture toughness.

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“…Numerical experimentations have shown that ~ at different increments may vary significantly within a single step. The magnitude of the variation is found to be influenced by types of relaxation techniques discussed in [6]. However, our results show that once the average G for a time step is determined, it is essentially independent of any relaxation techniques.…”

Section: G Calculation With Node Release Techniquementioning

confidence: 46%

“…Some frequently used methods are node release, moving singular element and shifting crack tip node techniques. The overview, including advantages and disadvantages, of these techniques was given by Atluri and Nishioka [6].…”

Section: Introductionmentioning

confidence: 99%

Computational analysis of dynamically propagating cracks in axisymmetric solids

Nakamura

1993

Int J Fract

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Dynamic crack propagation behavior in axisymmetric solids is investigated using an effective computational procedure. First, an accurate method to extract energy release rate of a dynamically propagating crack from finite element solutions is formulated for axisymmetric geometries. The method is applied to an analysis of a radially growing circular crack under remote tension in an infinite medium. The computed dynamic energy release rate shows an excellent agreement with the exact solution. Next, we have developed an iterative technique to propagate a crack whose velocity history is initially unknown. With the iterative procedure, the crack propagates according to a condition specified by a dynamic fracture criterion. At each increment of crack growth, an optimum velocity at which the crack growth condition satisfies is obtained by the iterative scheme. This procedure requires no artificial input or no preset crack tip speed in a simulation study. The iterative scheme is employed in a dynamic fracture analysis of ceramics. The computational analysis is carded out for simulation of fracture experiments using circumferentially notched round bars. In the test, a ceramic specimen is subjected to tensile stress wave loading and after crack growth initiation, the external crack propagates to tear the specimen. The computational simulation is carded out for the entire fracture process including the crack growth initiation and the dynamic propagation. The iterative procedure enables us to predict the crack tip velocity which is unmeasurable in the experiment. Suitabilities of proposed fracture toughness criteria for the ceramics are investigated by comparing measured and computed transmitted pulses through the uncracked ligament. This study proves the usefulness of the computational procedures for dynamic fracture analysis. It is most effective in characterizing dynamic fracture toughness where determination of every relevant parameter is difficult in the experiments.

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Numerical studies in dynamic fracture mechanics

Cited by 44 publications

References 35 publications

The Element Free Galerkin method for dynamic propagation of arbitrary 3-D cracks

The Element Free Galerkin method for dynamic propagation of arbitrary 3-D cracks

A spectral method for three-dimensional elastodynamic fracture problems

Computational analysis of dynamically propagating cracks in axisymmetric solids

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