Micromechanical Analysis of Heterogeneous Materials using FEMLAB

Drago, A., Pindera, M.J.
University of Virginia, Dept. of Civil Eng. & Applied Mechanics

A complete set of engineering moduli for two types of 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 in most cases asymptotically converge 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 fiber/matrix property contrast and on the particular modulus.

New results are presented which demonstrate departure from this bound ness rule and which highlight deviations from the generally accepted convergence rates of the apparent moduli to their effective values. In particular, not all effective engineering moduli are bounded by the apparent moduli obtained under homogeneous boundary conditions. Further, homogeneous displacement boundary conditions do not always produce better estimates of the effective moduli than homogeneous traction boundary conditions for all moduli.