Exact micromechanical analysis of composites with closely packed fibers

Abstract

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.