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Title: Exact micromechanical analysis of composites with closely packed fibers
Authors: Honein, Elie 
Honein, Tanios
Rai, Habib 
Najjar, Michel
Affiliations: Department of Mechanical Engineering 
Department of Mechanical Engineering 
Department of Mechanical Engineering 
Department of Mechanical Engineering 
Keywords: Fibers
Matrix algebra
Subjects: Aviation
Problem solving
Structural dynamics
Issue Date: 2018
Publisher: ARC
Part of: AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
Conference: AIAA/ASCE/AHS/ASC Structures,Structural Dynamics, and Materials Conference (8-12 January 2018 : Kissimmee, Florida) 
In this paper we show how a methodology based on the procedure of heterogenization can be implemented to solve the problem of an arbitrary number of fibers perfectly bonded to an infinite matrix which is subjected to arbitrary loading/singularities. At the heart of this methodology is a relation that exists between the solution of this heterogeneous problem and its corresponding homogeneous problem, i.e., the problem when the fibers are absent and the matrix material occupies the whole space while it is still being subjected to the same loading/singularities. This relation is universal in the sense of being independent of the loading considered. The methodology will be presented within the framework of anti-plane and plane elasticity. We proceed by considering the problem of a single fiber, then that of two fibers and we show how the result can be extended to solve for any number of fibers. This methodology leads to a new type of functional equations whose solutions are effected by novel techniques. Towards the end of the paper we touch upon the problem of two fibers in plane elasticity and we present the solution of two very challenging problems to show the efficacy of the method. © 2018, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.
Type: Conference Paper
Appears in Collections:Department of Mechanical Engineering

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