Stress concentration effects in micropolar elasticity

Kaloni, Puran N.; Ariman, T.

doi:10.1007/bf01593904

Cited by 69 publications

(40 citation statements)

References 9 publications

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“…Note that the couple tractions are homogeneous. It is well-known that the stress concentration factor around a circular hole is lower for Cosserat continuum than for the classical theory of elasticity [32].…”

Section: Stress Concentration In Cosserat Elasticitymentioning

confidence: 91%

“…The stress concentration is given as the ratio σ 11 /σ ∞ where σ ∞ is the stress component σ 11 far from the hole. The analytical solution for the stress concentration around a circular hole for the couple-stress theory has been derived in [34] and then extended to the Cosserat elasticity in [32], see also [17,35]. The stress concentration factor at the pole is equal to where…”

Section: Stress Concentration In Cosserat Elasticitymentioning

confidence: 99%

See 1 more Smart Citation

Hyper-reduction of generalized continua

Horák¹,

Ryckelynck²,

Forest³

2017

Comput Mech

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International audienceThis paper deals with the reduced order modeling of micromorphic continua. The reduced basis model relies on the proper orthogonal decomposition and the hyper-reduction. Two variants of creation of reduced bases using the proper orthogonal decomposition are explored from the perspective of additional micromorphic degrees of freedom. In the first approach, one snapshot matrix including displacement as well as micromorphic degrees of freedom is assembled. In the second approach, snapshots matrices are assembled separately for displacement and micromorphic fields and the singular value decomposition is performed on each system separately. Thereafter, the formulation is extended to the hyper-reduction method. It is shown that the formulation has the same structure as for the classical continua. The relation of higher order stresses introduced in micromorphic balance equations to creation of the reduced integration domain is examined. Finally, the method is applied to examples of microdilatation extension and clamped tension and to a size-dependent stress concentration in Cosserat elasticity. It is shown that the proposed approach leads to a good level of accuracy with significant reduction of computational time

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Section: Stress Concentration In Cosserat Elasticitymentioning

confidence: 91%

Section: Stress Concentration In Cosserat Elasticitymentioning

confidence: 99%

Hyper-reduction of generalized continua

Horák¹,

Ryckelynck²,

Forest³

2017

Comput Mech

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“…Studies of fracture processes in Cosserat materials were presented by Nakamura, Lakes and other researchers in [32,33,34,35]. Lakes showed that the solutions for stress concentration around circular and elliptic holes in plates and stress intensity factors for cracks in Cosserat solid are smaller than the same parameters in a classical solid.…”

Section: Development Of the Cosserat Theory Of Elasticitymentioning

confidence: 99%

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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“…); second the coordinate plane with a rigid inclusion ( Figure 5.c.). We remark that there exists an analytical solution for the stress concentration problem around the hole in an infinite plate of isotropic material if the stress state at infinity is t xx = p = constant = 100 n/mm 2 , t xy = t yx = t yy = µ xz = µ yz = 0, i.e., the plate is in tension [27,28,29]. The stress concentration factor K for the above problem can be calculated from the following equations: We have carried out the computation under the assumption that µ = 5 N/mm 2 , r o = 0.36 mm, ν = 0.0 (see Figure 6) or ν = 0.3 (see Figure 7).…”

Section: Examplesmentioning

confidence: 99%