P.A. Gourgiotis
Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity
Gourgiotis, P.A.; Georgiadis, H.G.
Authors
H.G. Georgiadis
Abstract
The present study aims at determining the elastic stress and displacement fields around the tips of a finite-length crack in a microstructured solid under remotely applied plane-strain loading (mode I and II cases). The material microstructure is modeled through the Toupin-Mindlin generalized continuum theory of dipolar gradient elasticity. According to this theory, the strain-energy density assumes the form of a positive-definite function of the strain tensor (as in classical elasticity) and the gradient of the strain tensor (additional term). A simple but yet rigorous version of the theory is employed here by considering an isotropic linear expression of the elastic strain-energy density that involves only three material constants (the two Lamé constants and the so-called gradient coefficient). First, a near-tip asymptotic solution is obtained by the Knein-Williams technique. Then, we attack the complete boundary value problem in an effort to obtain a full-field solution. Hypersingular integral equations with a cubic singularity are formulated with the aid of the Fourier transform. These equations are solved by analytical considerations on Hadamard finite-part integrals and a numerical treatment. The results show significant departure from the predictions of standard fracture mechanics. In view of these results, it seems that the classical theory of elasticity is inadequate to analyze crack problems in microstructured materials. Indeed, the present results indicate that the stress distribution ahead of the crack tip exhibits a local maximum that is bounded.
Citation
Gourgiotis, P., & Georgiadis, H. (2009). Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity. Journal of the Mechanics and Physics of Solids, 57(11), 1898-1920. https://doi.org/10.1016/j.jmps.2009.07.005
Journal Article Type | Article |
---|---|
Publication Date | Nov 1, 2009 |
Deposit Date | Sep 22, 2016 |
Publicly Available Date | Oct 3, 2016 |
Journal | Journal of the Mechanics and Physics of Solids |
Print ISSN | 0022-5096 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 57 |
Issue | 11 |
Pages | 1898-1920 |
DOI | https://doi.org/10.1016/j.jmps.2009.07.005 |
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Copyright Statement
NOTICE: this is the author's version of a work that was accepted for publication in Journal of the Mechanics and Physics of Solids. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of the Mechanics and Physics of Solids, 57, 11, November 2009, 10.1016/j.jmps.2009.07.005
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