The effect of couple stresses on the tip of a crack

Atkinson, C.; Leppington, F. G.

doi:10.1016/0020-7683(77)90080-4

Cited by 97 publications

(72 citation statements)

References 6 publications

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“…It is important to mention thatK I and L I are not independent [102,103]. As well, it should be stressed that the special stress intensity factors for the micropolar theory of elasticityK I andK II are distinct from the stress intensity factors of the classical theory of elasticity.…”

Section: Fracture Mechanics In the Cosserat Theory Of Elasticitymentioning

confidence: 98%

“…The first approach, which is adopted in this study, is based on the classical linear elastic fracture mechanics and assumes conventional I-III crack opening modes [102]. According to the second approach, the presence of the additional degrees of freedom leads to the cracks of higher modes IV-VI, also called bending cracks [96,97].…”

Section: Fracture Mechanics In the Cosserat Theory Of Elasticitymentioning

confidence: 99%

“…Depending on the α and γ values, the deviation ofK I from K I varies from 14% to 26%. The distributions ofK The first investigation in the area of fracture parameters in the Cosserat materials, such as stress concentration at the crack tip, was introduced in [103,102]. In both papers, the authors discussed the effect of the couple stresses on the stress concentration at a crack tip and the mechanical behaviour in the vicinity of a crack tip.…”

Section: Fracture Mechanics In the Cosserat Theory Of Elasticitymentioning

confidence: 99%

“…In both papers, it was demonstrated that the energy release rate tended to the classical result when the micropolar parameter tended to zero and the stress intensity factor did not. In addition, the authors of [102] discussed the path-independence of the contour integral for the micropolar (the Cosserat model with free rotations) and couple stress (the Cosserat model with constrained rotations) cases. First, for the case of the Cosserat continuum with constant rotations, the energy release rate tended to the classical result as the characteristic length tended to zero, and the energy release rate decreased as the micropolar (or couple-stress) parameter increased.…”

Section: Fracture Mechanics In the Cosserat Theory Of Elasticitymentioning

confidence: 99%

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Simulation of cracks in a Cosserat medium using the extended finite element method

Kapiturova

Gracie

Potapenko

2014

Mathematics and Mechanics of Solids

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This research investigates fracture behaviour in the Cosserat materials. The Cosserat elasticity description of the materials incorporates a characteristic length scale (e.g. grains, particles, fibres, etc.) into the model. The characteristic length scale in such materials is known to significantly influence the macroscopic behaviour of the whole body. Simulation of the fracture processes, such as crack opening and propagation, in Cosserat materials still remains a challenge for the scientific community. The goal of this thesis is to propose and validate a two dimensional extended finite element method model of edge cracks within the Cosserat elasticity theory framework.The crack modelling was conducted using the Finite Element Method (FEM) and eXtended Finite Element Method (XFEM) implemented in the Matlab code. The strong and weak formulations of the problem and the discrete XFEM equations are presented in the thesis. Mode I and II edge crack models in a Cosserat medium are discussed and verified through a series of patch and convergence tests. In addition, the numerical evaluation of the J-integral for the Cosserat medium is presented, and the J-integral for the Cosserat medium is compared to the J-integral for the classical elasticity.The XFEM/Cosserat method is shown to be robust and able to effectively model the edge crack problems in a Cosserat medium. Moreover, the elastic parameter α is found to be a powerful coupling tool between the microrotations and the translations. The Cosserat J-integral differs from the classical J-integral by 2% to 40%, for a given crack depending on the micropolar elastic coupling constant α.iii Acknowledgements I would like to thank my supervisors, Dr. Robert Gracie and Dr. Stanislav Potapenko, for their guidance and support during my study at the University of Waterloo.

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Section: Fracture Mechanics In the Cosserat Theory Of Elasticitymentioning

confidence: 98%

Section: Fracture Mechanics In the Cosserat Theory Of Elasticitymentioning

confidence: 99%

Section: Fracture Mechanics In the Cosserat Theory Of Elasticitymentioning

confidence: 99%

Section: Fracture Mechanics In the Cosserat Theory Of Elasticitymentioning

confidence: 99%

See 2 more Smart Citations

Simulation of cracks in a Cosserat medium using the extended finite element method

Kapiturova

Gracie

Potapenko

2014

Mathematics and Mechanics of Solids

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“…The same method was adopted by Ejike (1969) for a circular (penny-shaped) crack in couple-stress elasticity and by Sridharan (1980, 1981) for a finite-length crack in micropolar elasticity. Using the Wiener-Hopf technique, Atkinson and Leppington (1977) studied the problem of a semi-infinite crack with exponentially decayed normal tractions on the crack faces. More recently, Huang et al (1997) provided near-tip asymptotic fields for the mode I and mode II crack problems, in couplestress elasticity, by using the method of eigenfunction expansions.…”

Section: Introductionmentioning

confidence: 99%

Distributed dislocation approach for cracks in couple-stress elasticity: shear modes

Gourgiotis

Georgiadis

Defect and Material Mechanics

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Finite element analysis of plane couple‐stress problems using first order stress functions

Wood

1988

Numerical Meth Engineering

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SUMMARYA complementary energy based variational principle, using first order stress functions, is developed for plane linear elastic couple-stress problems. The principle is analogous to that used in a total potential energy based Mindlin/Reissner thick plate bending analysis and as such is a generalization of the classical analogy between plate stretching and plate bending. Traction boundary conditions are enforced using a Lagrange multiplier technique. The resulting Co finite element 'equilibrium stress model' is validated by investigating the reduction of the stress concentration factor associated with a small hole in a field of uniform tension.

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The effect of couple stresses on the tip of a crack

Cited by 97 publications

References 6 publications

Simulation of cracks in a Cosserat medium using the extended finite element method

Simulation of cracks in a Cosserat medium using the extended finite element method

Distributed dislocation approach for cracks in couple-stress elasticity: shear modes

Finite element analysis of plane couple‐stress problems using first order stress functions

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