A variational method for non-linear micropolar composites

Built upon Ponte Castañeda's method for a Cauchy medium, a variational method for evaluating the effective non-linear behavior of micropolar composites is proposed. The same as for a Cauchy medium, it is shown that the proposed variational method can be interpreted as the secant moduli method based on second-order stress and couple stress moments. With simple examples, the interplay between material length parameters of a higher-order medium and its geometrical dimensions and/or material constants is highlighted. By using the new variational method, the influence of reinforcement size on the yielding and strain hardening of particulate composites is examined in a simple and analytical manner. The predictions agree well with existing experimental data for selected particulate metal matrix composite systems. The particle size effect is found to be more pronounced for shear loading and hard particles.