Double virtual crack extension method for crack growth stability assessment

Suo, Xiao Zheng; Combescure, Alain

doi:10.1007/bf00035715

Cited by 19 publications

(16 citation statements)

References 11 publications

(16 reference statements)

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“…A stability analysis based on a second variation of the Lagrangian form (4) determines the most stable crack configuration evolution corresponding to that with the minimum energy dissipation [21,22]. The derivatives of the energy release rate with respect to the crack length [50,51], are computed by a generalized X-FEM formulation [21] of the FEM formulation developed by several authors [52][53][54]. All subdeterminants of this matrix [∂G i /∂ j ] are computed at time t n−1 and the maximum subdeterminant gives the set of tips N act that will grow at time step t n determined by:…”

Section: Description Of the Problemmentioning

confidence: 99%

Fracture strength assessment and aging signs detection in human cortical bone using an X-FEM multiple scale approach

2008

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We present a multiple scale approach for modeling multiple crack growth in human cortical bone under tension. The Haversian microstructure, a four phase composite, is discretized by a classical finite element method fed with the morphological and mechanical characteristics, experimentally measured, to mimic human bone heterogeneity at the micro scale. The fracture strength of human bone, exhibiting aging signs, is investigated through tensional percolation simulations in statistical microstructures. The cracks are initiated at the micro scale at locations where a critical elastic-damage strain-driven criterion is met. The cracks, modeled by the eXtended Finite Element Method, are then grown until complete failure when a critical stress intensity factor criterion is attained. The model provides the fracture strength and the global response at the material scale and the stress-strain fields at the microscopic level. The model creates a constitutive law at the material scale and emphasizes the influence of the microstructure on bone failure and fracture risk assessment. These results are validated against experiments.

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Section: Description Of the Problemmentioning

confidence: 99%

Fracture strength assessment and aging signs detection in human cortical bone using an X-FEM multiple scale approach

2008

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“…The problem of a finite plate with a center crack was studied [10]. The geometry of the plate is described in Fig.…”

Section: Center Crack In a Finite Platementioning

confidence: 99%

“…21. The analytical solution to this problem is given in Suo and Combescure [10]. The stress intensity factor is given by:…”

Section: Center Crack In a Finite Platementioning

confidence: 99%

An extended finite element method with higher-order elements for curved cracks

Stazi¹,

Budyn²,

Chessa³

et al. 2003

Computational Mechanics

199

147

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A finite element method for linear elastic fracture mechanics using enriched quadratic interpolations is presented. The quadratic finite elements are enriched with the asymptotic near tip displacement solutions and the Heaviside function so that the finite element approximation is capable of resolving the singular stress field at the crack tip as well as the jump in the displacement field across the crack face without any significant mesh refinement. The geometry of the crack is represented by a level set function which is interpolated on the same quadratic finite element discretization. Due to the higher-order approximation for the crack description we are able to represent a crack with curvature. The method is verified on several examples and comparisons are made to similar formulations using linear interpolants.

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“…In the first approach, Lin and Abel (1988) introduced a variational formulation in conjunction with a virtual crack extension technique (delorenzi, 1982, 1985Haber and Koh, 1985;Barbero and Reddy, 1990) (primarily used for calculating SIFs indirectly) to calculate the firstorder derivative of SIF for a single crack. Later, Suo and Combescure (1992) developed a double virtual crack extension method to calculate the first-order sensitivity of the energy release rate (ERR) with respect to the crack size. This method cleverly avoids calculation of the second-order derivative of the stiffness matrix and is applicable under combined loading conditions.…”

Section: Introductionmentioning

confidence: 99%

“…No mesh perturbation is necessary in the latter approach involving continuum shape sensitivity analysis. However, shape sensitivity methods available today (e.g., de Lorenzi, 1982de Lorenzi, , 1985Haber and Koh, 1985;Barbero and Reddy, 1990;Keum and Kwak, 1992;Suo and Combescure, 1992;Hwang et al, 1998;Feijóo et al, 2000;Taroco, 2000;Chen et al, 2001a, b;2002) are valid only for linear-elastic cracked structures. Since for some materials the nonlinear fracture-mechanics theory predicts more realistic fracture behavior than the linearelastic theory, there is a dire need to develop sensitivity equations for nonlinear-elastic cracked structures.…”

Section: Introductionmentioning

confidence: 99%

Continuum shape sensitivity and reliability analyses of nonlinear cracked structures

Rahman

Chen

2005

Int J Fract

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Abstract.A new method is proposed for shape sensitivity analysis of a crack in a homogeneous, isotropic, and nonlinearly elastic body subject to mode I loading conditions. The method involves the material derivative concept of continuum mechanics, domain integral representation of the J-integral, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is required in the proposed method. Since the governing variational equation is differentiated before the process of discretization, the resulting sensitivity equations are independent of any approximate numerical techniques. Based on the continuum sensitivities, the first-order reliability method was employed to perform probabilistic analysis. Numerical examples are presented to illustrate both the sensitivity and reliability analyses. The maximum difference between the sensitivity of stress-intensity factors calculated using the proposed method and the finite-difference method is less than four percent. Since all gradients are calculated analytically, the reliability analysis of cracks can be performed efficiently.

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Double virtual crack extension method for crack growth stability assessment

Cited by 19 publications

References 11 publications

Fracture strength assessment and aging signs detection in human cortical bone using an X-FEM multiple scale approach

Fracture strength assessment and aging signs detection in human cortical bone using an X-FEM multiple scale approach

An extended finite element method with higher-order elements for curved cracks

Continuum shape sensitivity and reliability analyses of nonlinear cracked structures

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