A Multi-scale Formulation for Smart Composites with Field Coupling Effects

Abstract

This study presents a two-scale homogenization scheme for determining effective thermal, mechanical, electrical, and piezoelectric properties of smart laminated composites. The studied smart composite is composed of a unidirectional fiber reinforced laminated system as a host structure and an active unidirectional fiber reinforced piezocomposite. The effective response of the composites, in a representative unit-cell model, is formulated based on a volume average of the field quantities of the constituents. Each unit-cell is divided into a number of subcells. A unit-cell model, consisting of four fiber and matrix subcells, is generated to homogenize mechanical and non-mechanical responses of a lamina. Material parameters in the constitutive models of the constituents, i.e., fiber and matrix, are allowed to vary with temperature and time. The macro-scale consists of a sublaminate model that homogenizes responses of representative layers in the laminated systems. Perfect bonds are assumed at the fiber–matrix interphases and at the interphases between laminae. The effective properties obtained from the present micromechanical model are comparable to the ones generated using an asymptotic homogenization scheme. Available experimental data in the literature are used to verify the multi-scale model formulation. The effects of temperature dependent material constants on the overall coupled electro-mechanical properties of composites during transient heat conduction are also examined.