Closed-form thermoelastic moduli of a periodic three-phase fiber-reinforced composite

In previous works, using the asymptotic homogenization method (AHM), analytical formulae have been obtained for all global elastic constants of a binary fiber composite with perfect interfaces. In many cases of interest the perfect interphase is not an adequate model and it is necessary to include in the analytical models one or more interphases separating the reinforcement inclusion phase from the host matrix phase. In this article, an extension of AHM to thermoelastic heterogeneous problems is given. A simple closed form of effective properties for a three-phase unidirectional transversely isotropic composite is presented. By using homogenization schemes for periodic media, the local problems are solved and effective thermoelastic properties moduli are determined. The method is based on the assumption that the scale ratio between the periodic cell and the whole composite tends to zero. New universal relations for the three-phase thermoelastic composite are found from the AHM. In order to analyze the interphase effect, the effective thermoelastic moduli are compared with some theoretical approaches and experimental results reported in the literature.