Linear thermoelastic higher-order theory for periodic multiphase materials

A new micromechanics model is presented which is capable of accurately esti mating both the effective elastic constants of a periodic multiphase compos ite and the local stress and strain fields in the individual phases. The mo del is presently limited to materials characterized by constituent phases t hat are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstruc ture. The models analytical framework is based on the homogenization techni que for periodic media, but the method of solution for the local displaceme nt and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite element solution method typically used i n conjunction with the homogenization technique. The present approach produ ces a closed-form macroscopic constitutive equation for a periodic multipha se material valid for both uniaxial and multiaxial loading which, in turn, can be incorporated into a structural analysis computer code. The models pr edictive accuracy is demonstrated by comparison with reported results of de tailed finite element analyses of periodic composites as well as with the c lassical elasticity solution for an inclusion in an infinite matrix.