Asymptotic homogenization of elastic composite materials with a regular structure

Abstract The objective of this paper is to apply the technique of asymptotic homogenization to determine the elastic behaviour of reinforced composite materials with unidirectional regular fibres. The analytical solution, which is based upon the complex potentials of Muskhelishvili, utilizes a series expansion of the doubly periodic Weierstrass elliptic functions to predict both the local and overall averaged properties of the composite material. Detailed analysis of both the plane and antiplane elastic problems are considered and the results are applied to a number of reinforced composites with varying mechanical properties and volume fractions. Comparison with existing extremal estimates and limiting cases of the properties are also considered and discussed.

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