Linear theory for the mechanics of third-gradient continua reinforced with fibers resistance to flexure
- Authors
- Bolouri, Seyed Ehsan Seyed; Kim, Chun I. L.; Yang, Seunghwa
- Issue Date
- Apr-2020
- Publisher
- SAGE PUBLICATIONS LTD
- Keywords
- Higher gradient elasticity; fiber-reinforced materials; flexure; superposed incremental deformations; plane deformations; triple forces
- Citation
- MATHEMATICS AND MECHANICS OF SOLIDS, v.25, no.4, pp 937 - 960
- Pages
- 24
- Journal Title
- MATHEMATICS AND MECHANICS OF SOLIDS
- Volume
- 25
- Number
- 4
- Start Page
- 937
- End Page
- 960
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/38013
- DOI
- 10.1177/1081286519893408
- ISSN
- 1081-2865
1741-3028
- Abstract
- A linear model, framed in the setting of the second strain gradient theory, is presented for the mechanics of an elastic solid reinforced with fibers resistant to flexure. The kinematics and bending resistance of the fibers are formulated via the second and third gradient of the continuum deformation. The corresponding Euler equations and admissible boundary conditions are then obtained by means of iterated integration by parts and variational principles arising in the third gradient of virtual displacement. In particular, within the prescription of superposed incremental deformations, we derive a compatible linear model from which a complete analytical solution describing the deformations of fiber composites is obtained. The proposed linear model predicts smooth and dilatational shear angle distributions over the domain of interest, which are also aligned with the results obtained from the corresponding nonlinear theory.
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- Appears in
Collections - College of Engineering > School of Energy System Engineering > 1. Journal Articles
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