Energy release rate calculations by the finite element method

deLorenzi, H. G.

doi:10.1016/0013-7944(85)90060-8

Cited by 166 publications

(56 citation statements)

References 10 publications

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“…deLorenzi [26,27] improved the method by considering the strain energy release rate of a continuum. The main advantages of the continuum approach are…”

Section: Virtual Crack Closure Techniquementioning

confidence: 99%

Strain Energy Release Rate Analysis of Adhesive-Bonded Composite Joints with a Prescribed Interlaminar Crack

Chadegani

Yang

Dan-Jumbo

2008

49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference &Amp;lt;br> 16th AIAA/ASME/AHS Ada

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“…deLorenzi [26,27] improved the method by considering the strain energy release rate of a continuum. The main advantages of the continuum approach are…”

Section: Virtual Crack Closure Techniquementioning

confidence: 99%

Strain Energy Release Rate Analysis of Adhesive-Bonded Composite Joints with a Prescribed Interlaminar Crack

Chadegani

Yang

Dan-Jumbo

2008

49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference &Amp;lt;br> 16th AIAA/ASME/AHS Ada

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“…2. The computation of J(s) has been performed using an equivalent domain integral, as proposed by Li et al (1985) and Shih et al (1986) (deLorenzi, 1982, 1985, obtained exactly the same result using the concept of virtual crack extension and a consistent continuum mechanics approach):…”

Section: Computation Of the J-integralmentioning

confidence: 99%

The Proper Generalized Decomposition (PGD) as a numerical procedure to solve 3D cracked plates in linear elastic fracture mechanics

Giner

Bognet

Ródenas

et al. 2013

International Journal of Solids and Structures

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ElsevierGiner Maravilla, E.; Bognet, B.; Ródenas García, JJ.; Fuenmayor Fernández, FJ.; Chinesta Soria, FJ. (2013) AbstractIn this work, we present a new approach to solve linear elastic crack problems in plates using the so-called Proper Generalized Decomposition (PGD). In contrast to the standard FE method, the method enables to solve the crack problem in an efficient way by obtaining a single solution in which the Poisson's ratio ν and the plate thickness B are non-fixed parameters. This permits to analyze the influence of ν and B in the 3D solutions at roughly the cost of a series expansion of 2D analyses.Computationally, the PGD solution is less expensive than a full 3D standard FE analysis for typical discretizations used in practice to capture singularities in 3D crack problems. In order to verify the effectiveness of the proposed approach, the method is applied to cracked plates in mode I with a straight-through crack and a quarter-elliptical corner crack, validating J-integral results with different reference solutions.

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“…In 1988, Lin and Abel [9] introduced a direct-integration approach for a virtual crack extension technique that employs the variational formulation and a ®nite element method (FEM) to calculate the ®rst derivative of SIF for a structure containing a single crack. This method maintains all of the advantages of similar virtual crack extension techniques introduced by deLorenzi [10,11], Haber and Koh [12], and Barbero and Reddy [13], but adds a capability to calculate the derivatives of the SIF. Subsequently, Hwang et al [14] generalized this method to calculate both ®rst-and secondorder derivatives for structures involving multiple crack systems, axisymmetric stress state, and crack-face and thermal loading.…”

Section: Introductionmentioning

confidence: 99%

Shape sensitivity analysis in mixed-mode fracture mechanics

Chen¹,

Rahman²,

Park

2001

Computational Mechanics

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This paper presents a new method for continuum-based shape sensitivity analysis for a crack in a homogeneous, isotropic, and linear-elastic body subject to mixed-mode (modes I and II) loading conditions. The method is based on the material derivative concept of continuum mechanics, domain integral representation of an interaction integral, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method to calculate the sensitivity of stress-intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations are independent of approximate numerical techniques, such as the ®nite element method, boundary element method, meshless methods, or others. In addition, since the interaction integral is represented by domain integration, only the ®rst-order sensitivity of the displacement ®eld is needed. Two numerical examples are presented to illustrate the proposed method. The results show that the maximum difference in the sensitivity of stress-intensity factors calculated using the proposed method and reference solutions obtained by analytical or ®nite-difference methods is less than four percent. IntroductionSensitivity analysis of a crack-driving force plays an important role in many fracture-mechanics applications involving the stability and arrest of crack propagation, reliability analysis, parameter identi®cation, or other considerations. For example, the derivatives of the stressintensity factor (SIF) or other fracture parameters are often required to predict the probability of fracture initiation and/or instability in cracked structures. The ®rst-and second-order reliability methods [1], frequently used in probabilistic fracture mechanics [2±8], require the gradient and Hessian of the performance function with respect to random parameters. In linear-elastic fracture mechanics (LEFM), the performance function is built on SIF. Hence, both ®rst-and/or second-order derivatives of SIF are needed for probabilistic analysis. The calculation of these derivatives with respect to load and material parameters, which constitutes size-sensitivity analysis, is not unduly dif®cult. However, the evaluation of response derivatives with respect to crack size is a challenging task, since it requires shape sensitivity analysis. Using a brute-force type ®nite-difference method to calculate the shape sensitivities is often computationally expensive, in that numerous repetitions of deterministic ®nite element analysis may be required for a complete reliability analysis. Furthermore, if the ®nite-difference perturbations are too large relative to ®nite element meshes, the approximations can be inaccurate, whereas if the perturbations are too small, numerical truncation errors may become signi®cant. Therefore, an important requirement of some fracture-mechanics applications is to evaluate the rates of SIF accurately and ef®ciently.Some methods have already appeared to predict the sens...

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Energy release rate calculations by the finite element method

Cited by 166 publications

References 10 publications

Strain Energy Release Rate Analysis of Adhesive-Bonded Composite Joints with a Prescribed Interlaminar Crack

Strain Energy Release Rate Analysis of Adhesive-Bonded Composite Joints with a Prescribed Interlaminar Crack

The Proper Generalized Decomposition (PGD) as a numerical procedure to solve 3D cracked plates in linear elastic fracture mechanics

Shape sensitivity analysis in mixed-mode fracture mechanics

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