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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Grahic Jump Location
Monopolar (external) and dipolar (internal) forces acting on an ensemble of subparticles in a material with microstructure
Grahic Jump Location
A crack under a remotely applied antiplane shear loading. The contour Γ surrounding the crack tip serves for the definition of the J-integral.
Grahic Jump Location
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
Grahic Jump Location
Branch cuts for the functions (β,γ)
Grahic Jump Location
Contour integrations for the factorization of the kernel function in Eq. (42)
Grahic Jump Location
Rectangular-shaped contour surrounding the crack tip for the evaluations of the J-integral and the energy release rate
Grahic Jump Location
Contour integration for the evaluation of the complex integral in Eq. (66)
Grahic Jump Location
Graphs of the exact gradient (total monopolar stress), asymptotic gradient (total monopolar stress), and classical KIII field solutions in normalized forms
Grahic Jump Location
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.
Grahic Jump Location
Branch cuts for the functions (β̄,γ̄)
Grahic Jump Location
Contour integrations for the factorization of the kernel function defined in Eq. (88)



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