On the unit cell for micromechanical analysis of fibre-reinforced composites

Abstract

This paper is concerned with the unit cell for micromechanical analyses of unidirectionally fibre-reinforced composites. A systematic consideration has been made to the symmetries present in idealised fibre-matrix systems. The symmetries enable the stresses, strains and displacements to be mapped from a unit cell to the whole field of interest. Appropriate boundary conditions of the unit cell have been derived from these symmetry considerations for micromechanical analyses. The loads to the unit cell and the responses of it in terms of macroscopic stresses or strains have been addressed in such a way that the effective properties of the material can be obtained from micromechanical analyses of the unit cell in a standard manner. No systematic account of this kind is available in the literature while the use of the unit cell for analyses of the microscopic behaviour of composite materials is becoming popular, in particular using finite elements, in order to obtain in–depth understanding of the performance of these materials. Ineffective introductions of the unit cell and incorrect applications of boundary conditions are often encountered. These have been clarified in this paper so that correct and effective use of the unit cell for micromechanical analyses can be achieved.