Closed-form expressions for effective viscoelastic properties of fiber-reinforced composites considering fractional matrix behavior

For determination of effective elastic properties of fiber-reinforced materials the so-called Chamis-equations are standardly used (Chamis, 1989). In this paper, these equations are extended towards viscoelasticity, making use of the correspondence principle (Lee, 1955). The determination of the effective properties takes place in the Laplace-Carson domain, with the back-transformation to the time domain being performed analytically, providing closed-form expressions for the effective viscoelastic behavior of the composite. Fractional viscoelastic models are used to describe the time-dependent behavior of the matrix, well-capturing the experimentally-observed viscoelastic behavior with a comparatively low number of parameters. The performance of the proposed determination of effective viscoelastic properties is assessed by means of alternative methods such as Eigenstrain-based methods and numerical simulations employing unit-cell (UC) models.