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Gradient Elasticity Modelling and Analysis for the Mechanics of Unidirectional and Bidirectional Fiber Reinforced Composites
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Modélisation et analyse de l'élasticité en gradient pour la mécanique des composites renforcés par fibres unidirectionnelles et bidirectionnelles
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- Author / Creator
- Zeidi, MohammadMahdi
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The mechanics of fiber-reinforced solids have consistently been the subject of intense study that significantly advances our knowledge and practice in materials science and engineering. The subject leads to two major branches of researches involving either the direct investigation of local behaviors of an individual fiber-matrix system including interfacial region or the development of continuum theory through which the overall microscopic behavior of fibers is adequately taken into account in the model of deformations. The former relies on massive identification procedures, which most often require huge computational resources. Nonetheless, this approach was used successfully in the analysis of the mechanics of composite materials. Continuum-based approaches offer the advantages of the continuum descriptions and the associated mathematical framework. In this thesis, a continuum-based model is presented for the mechanics of unidirectional and bidirectional composites subjected to finite plane deformations (flexure and extension). This is framed in the development of a constitutive relation within which the constraint of material incompressibility is augmented. The elastic resistance of the fibers is accounted for via the computation of variational derivatives along the lengths of fibers. The equilibrium equation and necessary boundary conditions are derived by virtue of the principles of virtual work statement. A rigorous derivation of the corresponding linear theory is developed and used to obtain analytical solution for small deformations superposed on large. Also, The solutions of the resulting Partial Differential Equations (PDEs) are obtained using the Finite Element Analysis (FEA), which demonstrate excellent correspondence with existing theoretical and experimental results. The numerical results are compared with the results in literatures (FEniCS Project) showing a good agreement. The proposed model can serve as an alternative 2D Cosserat theory of nonlinear elasticity.
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- Graduation date
- Fall 2018
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- Type of Item
- Thesis
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- Degree
- Master of Science
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- License
- Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.