Strength of periodic elastic-brittle composites evaluated through homogenization and parameter identification

Reference is made herein to the elastic–brittle behavior of unidirectional E-glass-fiber epoxy–matrix composites of potential use in offshore technology. In view of engineering analyses of structural components, an anisotropic constitutive model in average stresses and strains is selected, centered on an elastic stiffness tensor and on an elastic limit locus and a strength locus in the average stress space. These loci are here described according to the popular Tsai–Wu model, and to a trigonometric model characterized by a user-chosen number of parameters as proposed by Labossière and Neale. The identification of the coefficients in the analytical expressions of both loci is performed by solving a mathematical programming problem, apt to minimize a norm which quantifies the discrepancy between the elastic limit or the peak stress computed by micromechanical homogenization (or defined by experimental data, if available) on one side and the relevant predictions (as functions of those coefficients) by the macroscopic model on the other side. The selection of the radial paths in the average stress or average strain space, based herein on the mathematical theory of regular polytopes, turns out to be crucial factor for the cost-effectiveness of the parameter identification process. The proposed methodology is discussed by means of examples related to practical engineering situations.