A generalized micromechanics model with shear-coupling

Abstract

A unified mathematical framework for a higher-order transverse shear-normal stress coupled micromechanical model is presented. The model is developed based on the analysis of a repeating unit cell in a doubly periodic array of fibers. The behavior in subregions within the unit cell is modeled using an expansion for the displacement field. The order and form of the displacement expansions in the subregions are arbitrary. The higher-order terms in the displacement expansion result in coupling between the transverse shearing and the normal deformation responses (shear coupling). The formulation is sufficiently general to allow generic elastic, plastic, viscoelastic, viscoplastic, or damage constitutive models (within the context of infinitesimal strain theory) for history-dependent behavior to be incorporated into the micromechanical framework. The proposed approach is analytical and provides closed-form expressions for the effective macroscopic behavior of a continuous fiber composite.