Frequency domain homogenization of effective and localized viscoelastic response of unidirectional composites with imperfect interfaces

Abstract

The locally-exact homogenization theory for unidirectional periodic composites with imperfect interfaces is generalized to estimate the effective complex moduli of viscoelastic composites in the frequency domain and recover corresponding localized stress distributions. In order to avoid complex mesh discretization, the Trefftz concept is adopted to obtain the analytical expression of internal displacements and stresses of representative unit cells by directly solving elastic partial differential equations. Physical coating and linear cohesive spring models are implemented at the interface between fibers and matrix. Besides, we also prove that the two imperfect interface models are equivalent under specified viscoelastic conditions. Comparisons against simulations available in the literature are given to validate the present method where good agreement is generally obtained. The effects of phase volume fraction, coating thickness and interfacial stiffness on five independent elastic constants are effectively investigated using the present models, further the local stress distributions within unit cells are presented to illustrate the effect of imperfect interfaces on material properties. Finally, the free vibration of Euler beams composed of unidirectional composites are studied through multiscale simulations to demonstrate importance of aforementioned microstructural parameters on damping of structural vibration, offering guideline for the structural and material design of aircrafts and satellites.