A complete set of engineering moduli for unidirectional composites with large fiber/matrix property contrasts was generated using the finite-element approach based on three sets of boundary conditions employed to calculate macroscopic moduli of statistically homogeneous and periodic heterogeneous materials. The boundary condition-dependent differences in the generated moduli highlight the differences between representative volume element and repeating unit cell concepts, which continue to be used interchangeably in the composite mechanics community. Homogeneous boundary conditions, which underpin the concept of a representative volume element, produce apparent engineering moduli that, typically, converge asymptotically to effective moduli of a periodic composite from below and above with increasing number of uniformly-spaced inclusions at a rate that depends on the inclusion/matrix property contrast and on the particular modulus. Herein, new results are presented which demonstrate that not all effective engineering moduli are bounded by the apparent moduli obtained under homogeneous displacement and traction boundary conditions. Further, the quality of the effective moduli estimates depends both on the type of homogeneous boundary conditions and the particular engineering modulus regardless of the inclusion/matrix property mismatch.
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