Modeling mixed-mode dynamic crack propagation nsing finite elements: Theory and applications

Swenson, Daniel; Ingraffea, Anthony R.

doi:10.1007/bf00301139

Cited by 166 publications

(96 citation statements)

References 17 publications

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“…Furthermore, in the case under consideration, the secant matrix S X i n+1 is symmetric. Comparing expressions (22) and (25) it is obvious that both methods can be implemented similarly, the only difference being the use of the tangent or secant matrix.…”

Section: Algebraic Implementation Aspectsmentioning

confidence: 99%

“…Details on the algebraic tangent system of equations (22) are given in references [37,36]. The algebraic secant system of equations (25) reads:…”

Section: Algebraic Implementation Aspectsmentioning

confidence: 99%

“…Initially, local remeshing of the elements in the vicinity of the crack was used [22,23]. Simo [24,25] proposed the enhanced strain elements, which take into account a local decomposition of the strains in compatible and incompatible modes.…”

Section: Introductionmentioning

confidence: 99%

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3D numerical modelling of twisting cracks under bending and torsion of skew notched beams

Benedetti

Cervera

Chiumenti

2017

Engineering Fracture Mechanics

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The testing of mode III and mixed mode failure is every so often encountered in the dedicated literature of mechanical characterization of brittle and quasi-brittle materials. In this work, the application of the mixed strain displacement ε − u finite element formulation to three examples involving skew notched beams is presented. The use of this FE technology is effective in problems involving localization of strains in softening materials.The objectives of the paper are: (i) to test the mixed formulation in mode III and mixed mode failure and (ii) to present an enhancement in terms of computational time given by the kinematic compatibility between irreducible displacement-based and the mixed strain-displacement elements.Three tests of skew-notched beams are presented: firstly, a three point bending test of a PolyMethyl MethaAcrylate beam; secondly, a torsion test of a plain concrete prismatic beam with square base; finally, a torsion test of a cylindrical beam made of plain concrete as well. To describe the mechanical behavior of the material in the inelastic range, Rankine and Drucker-Prager failure criteria are used in both plasticity and isotropic continuum damage formats.The proposed mixed formulation is capable of yielding results close to the experimental ones in terms of fracture surface, peak load and global loss of carrying capability. In addition, the symmetric secant formulation and the compatibility condition between the standard irreducible method and the strain-displacement one is exploited, resulting in a significant speedup of the computational procedure.

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Section: Algebraic Implementation Aspectsmentioning

confidence: 99%

“…Details on the algebraic tangent system of equations (22) are given in references [37,36]. The algebraic secant system of equations (25) reads:…”

Section: Algebraic Implementation Aspectsmentioning

confidence: 99%

See 1 more Smart Citation

3D numerical modelling of twisting cracks under bending and torsion of skew notched beams

Benedetti

Cervera

Chiumenti

2017

Engineering Fracture Mechanics

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“…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

202

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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“…rock, concrete, ceramics, etc. Many models have been developed in the field of computational fracture mechanics, such as linear and nonlinear elastic fracture mechanics based methods (Bittencourt et al, 1996;Ingraffea and Manu, 1980;Swenson and Ingraffea, 1988), the extended finite element method (XFEM) (Belytschko and Black, 1999;Karihaloo and Xiao, 2003;Melenk and Babuška, 1996;Sukumar and Prévost, 2003), the cohesive-zone model (Bocca et al, 1991;de Borst, 2003) and meshless methods, such as the element free Galerkin method (EFGM) (Bordas et al, 2008;Fleming et al, 1997). Moreover, discontinuumbased numerical methods that are originally used for granular materials, such as the smoothed particle hydrodynamics (SPH) method (Das and Cleary, 2010;Gray et al, 2001;Ma et al, 2011) and the discrete element method (DEM) (Cundall and Strack, 1979;Morris et al, 2004;Shi and Goodman, 1985) have also become increasingly popular in fracture modelling.…”

Section: Methodsmentioning

confidence: 99%

A numerical study of fracture spacing and through-going fracture formation in layered rocks

Guo

Latham

Xiang

2017

International Journal of Solids and Structures

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Naturally fractured reservoirs are an important source of hydrocarbons.Computational models capable of generating fracture geometries according to geomechanical principles offer a means to create a numerical representation of a more realistic rock mass structure. In this work, the combined finite-discrete element method is applied to investigate fracture patterns in layered rocks. First, a three-layer model undergoing layer normal compression is simulated with the aim of examining the controls on fracture spacing in layered rocks. Second, a seven-layer model with low competence contrast is modelled under direct tension parallel to the layering and bending conditions with the focus on investigating through-going fracture formation across layer interfaces. The numerical results give an insight into the understanding of various mechanisms that contribute to fracture pattern development in layered rocks.

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Modeling mixed-mode dynamic crack propagation nsing finite elements: Theory and applications

Cited by 166 publications

References 17 publications

3D numerical modelling of twisting cracks under bending and torsion of skew notched beams

3D numerical modelling of twisting cracks under bending and torsion of skew notched beams

A spectral method for three-dimensional elastodynamic fracture problems

A numerical study of fracture spacing and through-going fracture formation in layered rocks

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