Finite element modulation of effective viscoelastic properties of unilateral composite materials

We propose a method for calculating effective viscoelastic properties of composite materials under steady-state cyclical vibrations. The method is based on asymptotic averaging of periodic structures and finite-element solution of local problems of viscoelasticity in periodicity cells of composite materials. We provide examples of numerical simulation of viscoelastic properties for composites with unidirectional reinforcement, and of calculations of complex tensors of stress concentration in a periodicity cell. The paper presents a comparative analysis of dependencies of loss tangent of complex composite elasticity modulus on vibration frequencies obtained through FEA calculations and rough mixed formulae. We show that rough mixed formulae, often used for calculating dissipative properties of composite materials, can yield appreciable calculation errors.