Askes, H., Suiker, A.S.J. and Sluys, L.J. (2001) A classification of higher-order strain gradient models - linear analysis. Archive of Applied Mechanics, 72 (2). 171 - 188. ISSN 0939-1533
Abstract
The use of higher-order strain-gradient models in mechanics is studied. First, existing second-gradient models from the literature are investigated analytically. In general, two classes of second-order strain-gradient models can be distinguished: one class of models has a direct link with the underlying microstructure, but reveals instability for deformation patterns of a relatively short wave length, while the other class of models does not have a direct link with the microstructure, but stability is unconditionally guaranteed. To combine the advantageous properties of the two classes of second-gradient models, a new, fourth-order strain-gradient model, which is unconditionally stable, is derived from a discrete microstructure. The fourth-gradient model and the second-gradient models are compared under static and dynamic loading conditions. A numerical approach is followed, whereby the element-free Galerkin method is used. For the second-gradient model that has been derived from the microstructure, it is found that the model becomes unstable for a limited number of wave lengths, while in dynamics, instabilities are encountered for all shorter wave lengths. Contrarily, the second-gradient model without a direct link to the microstructure behaves in a stable manner, although physically unrealistic results are obtained in dynamics. The fourth-gradient model, with a microstructural basis, gives stable and realistic results in statics as well as in dynamics.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Copyright Springer-Verlag 2002. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | Strain-gradient Models; Higher-order Continuum; Microstructure; Wave Propagation; Stability |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 07 Oct 2015 14:48 |
Last Modified: | 07 Oct 2015 14:48 |
Published Version: | https://doi.org/10.1007/s00419-002-0202-4 |
Status: | Published |
Publisher: | Springer Verlag |
Refereed: | Yes |
Identification Number: | 10.1007/s00419-002-0202-4 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:85973 |