On selection of repeated unit cell model and application of unified periodic boundary conditions in micro-mechanical analysis of composites

Most micro-mechanical analyses for composites are based on repeated unit cell models (RUCs) by assuming a periodical distribution of the reinforcing phase. In this paper, the uniqueness of solution by applying unified displacement-difference periodic boundary conditions on the RUCs has been proved. Further it is deduced that (1) selection of the RUCs for a fixed periodic array may not be unique, however, the solution is independent on the choice of the different RUCs; (2) boundary traction continuity conditions can be guaranteed by the application of the proposed unified displacement-difference periodic boundary conditions. Illustrative examples are presented and advantages of applying this type of unified periodic boundary conditions are discussed.