Sensitivity of responses of three micro-mechanics approaches to changes in unit cell configuration and inclusion shape

Abstract

We use three micromechanics approaches, namely, the method of cells (MoCs), the Fourier series approach (FSA) and the transformation field analysis (TFA) to delineate the sensitivity of their predictions to changes in the unit cell configuration. The three approaches are formulated to have identical final expressions relating the local sub-cell strains to the homogenized strains in the unit cell. The cubic-edge, the hexagonal close-packed and the cubic-diagonal unit cell configurations are employed to study the elasto-plastic response of a Boron-Aluminum fiber reinforced composite under transverse loading, and compare present results with Brockenbrough et al.’s findings who used the finite element method. The elasto-plastic response predicted from the cubic-edge unit-cell shows the most hardening while that from the cubic-diagonal unit-cell the least hardening. Of the three approaches employed, the elasto-plastic response predicted by the MoCs is closest to that of Brockenbrough et al. The effect of fiber cross section on the elasto-plastic response analyzed using only the TFA approach is found to be significant for both elastic constants and plastic hardening.