Modeling of time and frequency dependent behavior of viscoelastic multi-layered reinforced composites with imperfect interfaces

In this work, a two-step homogenization strategy is developed to predict the frequency and time-dependent effective behavior of multi-layered reinforced viscoelastic composites with imperfect interfaces.In the first step, the modeling is based on the extension of a matrix formulation, initially developed for multi-layered elastic composites with perfect interfaces, to the case of multi-layered viscoelastic composites with imperfect interfaces.This extension is made by using the Laplace Carson transform to transform the linear viscoelastic constitutive law to another one analogous to the elastic one and an adapted linear spring model for viscoelastic imperfect interfaces.In the second step, the well-known Mori-Tanaka micromechanical model is used to estimate the effective behavior of each reinforced layer.The estimated effective behavior is injected into the developed matrix formulation to obtain the effective behavior of the considered multi-layered composite.The effective behavior is estimated both in the frequency and time domains.For comparison, a perfect hybrid model in which the interface is considered as an interlayer with an equivalent thickness is considered.Numerical results are presented in the frequency and time domains with respect to constituent volume fractions and imperfect interface effects.The developed approach allows one to design multi-layered viscoelastic composites taking into account the geometric and mechanical parameters of constituents.