A generalized micromechanics model with shear-coupling

Summary

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.

The model is validated by comparison with existing micromechanics models. The agreement between the predicted effective moduli obtained from the current model and other existing models indicates that the current formulation accurately predicts the effective elastic behavior of a composite. Furthermore, comparison with existing data for the local elastic stress distributions around the inclusion indicates that the current model correctly captures the trends and magnitudes in these distributions. The predictions obtained from the current theory are shown to be more accurate than the corresponding MOC predictions. The ability to more accurately capture the spatial stress distributions can be directly attributed to the incorporation of the shear-coupling phenomena.

Finally, the influence of the presence of shear coupling on the local field distributions is considered for the simple macroscopic loading cases of transverse tension and transverse shearing. It is shown that signficant coupling between the local transverse shearing and normal deformation responses exists even when the composite is subjected to a macroscopically simple loading field. The existence of this coupling has potentially significant implications in the implementation of history-dependent constitutive models.