On the strain gradient bending deformations
Bending deformations are reviewed in the context of strain gradient linear elasticity, considering the complete set of strain gradient components. It is well understood that conventional bending deformations depend on the collective uniaxial extension of axial fibers resulting in the dependence on t...
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2013-04-01
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Online Access: | https://doi.org/10.1515/jmbm-2013-0006 |
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doaj-d38dc6f8a05344528af3c52d41af45872021-10-02T19:26:16ZengDe GruyterJournal of the Mechanical Behavior of Materials0334-89382191-02432013-04-01215-618118610.1515/jmbm-2013-0006On the strain gradient bending deformationsLazopoulos Konstantinos A.0Lazopoulos Anastasios K.1School of Mathematical Sciences (SEMFE), National Technical University of Athens, 5 Heroes of Polytechnion Avenue, Athens 15573, GreeceMathematical Sciences Department, Hellenic Army Academy, Vari 16673, GreeceBending deformations are reviewed in the context of strain gradient linear elasticity, considering the complete set of strain gradient components. It is well understood that conventional bending deformations depend on the collective uniaxial extension of axial fibers resulting in the dependence on the curvature of the neutral geometry of various (linear or surface) structures. Nevertheless, the deformation of each fiber depends not only on the local curvature of the neutral geometry but also on the distance of the fiber from the neutral axis. Hence, the strain gradient tensor of the conventional bending strain should include not only components along the neutral axis but also those on the transverse direction. The problems of bending and buckling, along with geometrically non-linear and post-critical behavior, are reviewed in the context of strain gradient elasticity considering not only conventional bending strain but also the complete components of the strain gradient.https://doi.org/10.1515/jmbm-2013-0006bendingbucklinggradient elasticity |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lazopoulos Konstantinos A. Lazopoulos Anastasios K. |
spellingShingle |
Lazopoulos Konstantinos A. Lazopoulos Anastasios K. On the strain gradient bending deformations Journal of the Mechanical Behavior of Materials bending buckling gradient elasticity |
author_facet |
Lazopoulos Konstantinos A. Lazopoulos Anastasios K. |
author_sort |
Lazopoulos Konstantinos A. |
title |
On the strain gradient bending deformations |
title_short |
On the strain gradient bending deformations |
title_full |
On the strain gradient bending deformations |
title_fullStr |
On the strain gradient bending deformations |
title_full_unstemmed |
On the strain gradient bending deformations |
title_sort |
on the strain gradient bending deformations |
publisher |
De Gruyter |
series |
Journal of the Mechanical Behavior of Materials |
issn |
0334-8938 2191-0243 |
publishDate |
2013-04-01 |
description |
Bending deformations are reviewed in the context of strain gradient linear elasticity, considering the complete set of strain gradient components. It is well understood that conventional bending deformations depend on the collective uniaxial extension of axial fibers resulting in the dependence on the curvature of the neutral geometry of various (linear or surface) structures. Nevertheless, the deformation of each fiber depends not only on the local curvature of the neutral geometry but also on the distance of the fiber from the neutral axis. Hence, the strain gradient tensor of the conventional bending strain should include not only components along the neutral axis but also those on the transverse direction. The problems of bending and buckling, along with geometrically non-linear and post-critical behavior, are reviewed in the context of strain gradient elasticity considering not only conventional bending strain but also the complete components of the strain gradient. |
topic |
bending buckling gradient elasticity |
url |
https://doi.org/10.1515/jmbm-2013-0006 |
work_keys_str_mv |
AT lazopouloskonstantinosa onthestraingradientbendingdeformations AT lazopoulosanastasiosk onthestraingradientbendingdeformations |
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1716846784886603776 |