A Complex Potential Approach to Micromechanics of Unidirectional Composites

Abstract

Complex potential methods for the solution of two-dimensional boundary value problems in linear elasticity are used to perform micromechanics analysis of unidirectional composites. The composite microstructure is idealized as a square array of unit cells subjected to prescribed strains. Unit cell analyses are performed for plane strain and anti-plane strain conditions to study the interaction of the fiber and matrix materials. The unit cell solutions are used to derive predictions for the ply moduli, Poisson’s ratios and coefficients of thermal expansion, which are shown to agree with the results of other methods. Applications to strength prediction are briefly discussed, and the detailed stress field results that can be generated using the approach are illustrated.