A time dependent model for unidirectional fibre-reinforced composites with viscoelastic matrices

In this work, a fully three-dimensional constitutive model suitable for the macroscopic description of unidirectional fibre-reinforced composites where the matrix exhibits a time-dependent viscoelastic behaviour is developed. Specifically, we consider a coordinate-free formulation where the stress and strain fields can be decomposed into fibre-directional and volumetric parts on the one hand, and into extra contributions on the other hand. This offers an ideal framework where one can separate the fibres’ contribution, considered here as time-independent and linearly elastic, and the matrix contribution that experiences creep only in shear. Among the many possibilities, we choose in this work a generalized Kelvin-Voigt rheological model to formulate the viscoelastic behaviour of the matrix. Long-term as well as short-term relaxation processes can be integrated in the model by means of as many as necessary viscoelastic processes. The numerical discretization is described for an easy intergration within a finite element procedure. Finally, numerical examples illustrate the possibilities of the present model.