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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 displacementdifference 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.

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A series of uniaxial cyclic tests were carried out on solid cylindrical specimens of an epoxy resin, Epon 826/Epi-Cure Curing Agent 9551. The focus of the study was to investigate time-dependent viscoelastic behavior of this thermosetting polymer material under cyclic loading and to develop a constitutive model with the capabilities to simulate the observed deformation response. The tests include stress-controlled or strain-controlled cyclic loading with/without mean stress or mean strain at various amplitudes and loading rates. It was found that the cyclic stress-strain response of this material is amplitude-dependent and rate-dependent, and the response to axial tension is different from that in compression. The stress-strain loops exhibit more pronounced nonlinearity with high amplitudes or low loading rates. For stress-controlled cyclic loading with mean stress, ratcheting strain is accumulated, which is of viscoelastic nature, and this is confirmed by its full recovery after load removal. For strain-controlled cyclic loading with mean strain, the mean stress relaxation occurs, which contributes to the observed longer life in comparison to the stress-controlled cyclic loading with mean stress. Polym. Eng. Sci