Cell model for homogenization of fiber-reinforced composites: General theory and nonlinear elasticity effects

摘要

The theoretical basis of the homogenization technique developed by Aboudi is presented and assessed. Given the constitutive relations of the constituents, this technique provides an equivalent, homogeneous, constitutive model of unidirectional, continuous-fiber-reinforced composites. The expressions that comprise the first-order version of the technique are given special attention as this treatment has considerable practical value. Nonlinear elasticity effects are added to it. This extension increases the accuracy of numerical simulations of high strain-rate loadings. It is particularly important for any dynamic loading in which shock waves might be produced, including crash safety, armor, and munitions applications. Examples illustrate that elastic nonlinearity can make substantial contributions at strains of only a few per cent. These contributions are greatest during post-yield inelastic deformation. The micromechanics-based homogenization technique is shown to facilitate use of an efficient approximate treatment of elastic nonlinearity in composites with isotropic matrix materials.