Bounds on the overall elastic and instantaneous elastoplastic moduli of periodic composites

Abstract Bounds on the overall elastic and instantaneous elastoplastic moduli of composites with periodic microstructures are found using the extremum principles of Hashin and Shtrikman (1962) and the analytic solution of Nemat-Nasser et al. (1982). The bounds contain terms which depend on the geometric properties of the constituent materials and the corresponding interaction effects. Examples are presented for composites whose constituents are elastically isotropic having isotropic and kinematic plastic hardening responses.