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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Main Authors: Lazopoulos Konstantinos A., Lazopoulos Anastasios K.
Format: Article
Language:English
Published: De Gruyter 2013-04-01
Series:Journal of the Mechanical Behavior of Materials
Subjects:
Online Access:https://doi.org/10.1515/jmbm-2013-0006
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spelling 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
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