General unit cells for micromechanical analyses of unidirectional composites

Abstract

Two typical idealised packing systems have been employed for unidirectionally fibre reinforced composites, viz. square and hexagonal ones. A systematic approach has been adopted and it involves the use of only the translational symmetry transformations. There are a number of important advantages resulting from this. The unit cells so derived are capable of accommodating fibres of irregular cross-sections and imperfections asymmetrically distributed around fibres such as microcracks and local debonding in the system, provided the regularity of the packing and imperfections is present. Furthermore, all the unit cells established can be subjected to arbitrary combinations of macroscopic stresses or strains unlike most available unit cells in the literature which can only deal with individual macroscopic stress or strain components. Boundary conditions for these unit cells have been derived from appropriate considerations of the conditions of symmetry transformations. Applications of macroscopic stresses or strains as the loads to the unit cells have been described in such a way that they can be implemented in a straightforward manner and the effective properties of the composite can be evaluated following a standard procedure.