Outside of the classical microstructural detail-free estimates of effective moduli, micromechanical analyses of macroscopically uniform heterogeneous media may be grouped into two categories based on different geometric representations of material microstructure. Analysis of periodic materials is based on the repeating unit cell (RUC) concept and the associated periodic boundary conditions. This contrasts with analysis of statistically homogeneous materials based on the representative volume element (RVE) concept and the associated homogeneous boundary conditions. In this paper, using the above classification framework we provide a critical review of the various micromechanical approaches that had evolved along different paths, and outline recent emerging trends. We begin with the basic framework for the solution of micromechanics problems independent of microstructural representation, and then clarify the often confused RVE and RUC concepts. Next, we describe classical models, including the available RVE-based models, and critically examine their limitations. This is followed by discussion of models based on the concept of microstructural periodicity. In the final part, two recent unit cell-based models, which continue to evolve, are outlined. First, a homogenization technique called finite-volume direct averaging micromechanics theory is presented as a viable and easily implemented alternative to the mainstream finite-element based asymptotic homogenization of unit cells. The recent incorporation of parametric mapping into this approach has made it competitive with the finite-element method. Then, the latest work based on locally-exact solutions of unit cell problems is described. In this approach, the interior unit cell problem is solved exactly using the elasticity approach. The exterior problem is tackled with a new variational principle that successfully overcomes the non-separable nature of the overall unit cell problem.

Micromechanics of spatially uniform heterogeneous media: A critical review and emerging approaches

Several analyses for predicting the longitudinal, alpha(1), and transverse, alpha(2), coefficients of thermal expansion of unidirectional composites were compared with each other, and with experimental data on different graphite fiber reinforced resin, metal, and ceramic matrix composites. Analytical and numerical analyses that accurately accounted for Poisson restraining effects in the transverse direction were in consistently better agreement with experimental data for alpha(2), than the less rigorous analyses. All of the analyses predicted similar values of alpha(1), and were in good agreement with the experimental data. A sensitivity analysis was conducted to determine the relative influence of constituent properties on the predicted values of alpha(1), and alpha(2). As would be expected, the prediction of alpha(1) was most sensitive to longitudinal fiber properties and the prediction of alpha(2) was most sensitive to matrix properties.

Prediction of Coefficients of Thermal Expansion for Unidirectional Composites

Bilinear stress-strain relation of symmetric, [0/90] composite laminates is shown to be associated with gradual, not complete, degradation of 90° layers. Difference between the complete failure model and gradual failure model is discussed, complemented by pertinent experimental evidences. Experimental data on glass/epoxy and graphite/epoxy cross-ply laminates are compared with the theoretical predictions. The effect of strain biaxiality on failure of 90° layers is shown to be negligible when the laminate is subjected only to a uniaxial tension.

On the Behavior of Composite Laminates After Initial Failures

A micromechanical model for plastic behavior of fibrous composites

Thermal expansion of metal-matrix composites

This paper and a subsequent one will present the results of an investiga tion which analytically relates the fiber/matrix nonlinearities to the post- yielding behavior of symmetric laminates made from unidirectional plies. This first paper is primarily concerned with the behavior of the single ply and the means for anticipating its response within a laminate. Boron and carbon/epoxies are considered along with a metal matrix composite. The qualitative features of the response of these unidirectional materials to normal, shear, and combined loads are discussed. The analysis (based on triangular finite element idealizations of regularly-spaced inclusion arrays) anticipates the level of nonlinearity that has been observed in composite shear and transverse tensile tests. Also, it reveals a nonlinear coupling that may exist between the combined shear and normal stress response.

Raymond L. Foye

Papers

Theoretical Post-Yielding Behavior of Composite Laminates Part II-Inelastic Macromechanics