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TECHNICAL PAPERS

The Mode III Crack Problem in Microstructured Solids Governed by Dipolar Gradient Elasticity: Static and Dynamic Analysis

[+] Author and Article Information
H. G. Georgiadis

Mechanics Division, National Technical University of Athens, 1 Konitsis Street, Zographou GR-15773, Greece e-mail: georgiad@central.ntua.gr

J. Appl. Mech 70(4), 517-530 (Aug 25, 2003) (14 pages) doi:10.1115/1.1574061 History: Received April 28, 2002; Revised December 19, 2002; Online August 25, 2003
Copyright © 2003 by ASME
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References

Figures

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Monopolar (external) and dipolar (internal) forces acting on an ensemble of subparticles in a material with microstructure
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A crack under a remotely applied antiplane shear loading. The contour Γ surrounding the crack tip serves for the definition of the J-integral.
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William’s method: the near-tip fields of (i) a finite length crack, (ii) an edge crack, and (iii) a cracked strip correspond to the field generated in a body with a semi-infinite crack
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Branch cuts for the functions (β,γ)
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Contour integrations for the factorization of the kernel function in Eq. (42)
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Rectangular-shaped contour surrounding the crack tip for the evaluations of the J-integral and the energy release rate
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Contour integration for the evaluation of the complex integral in Eq. (66)
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Graphs of the exact gradient (total monopolar stress), asymptotic gradient (total monopolar stress), and classical KIII field solutions in normalized forms
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Variation of the exact total monopolar stress (according to the gradient theory) with (x/h) for the cases c=h2 and c=(0.01h)2. The graphs depict that the cohesive zone is small as compared to the intrinsic material length h and that the stress ahead of the cohesive zone exhibits a bounded maximum.
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Branch cuts for the functions (β̄,γ̄)
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Contour integrations for the factorization of the kernel function defined in Eq. (88)

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