Mechanism-based modelling of the viscoelastic response of a unidirectional composite ply: validation of a new transversely isotropic model through analytical and numerical homogenisation

The viscoelastic response of long fibres, polymer matrix composites is mainly due to the deviatoric response of the matrix. This single microscale mechanism, however, results in different amount of viscous relaxation for the elastic constants defining the transversely isotropic behaviour at the scale of the composite ply. In a recent work, some of the authors proposed a reformulation of transverse isotropy based on the Cartan decomposition. This geometrical formulation of the constitutive law leads to a set of five elastic parameters which is different from those commonly used in the formulation of constitutive laws, but which is easier to relate to the underlying constituents. In particular, only two of the parameters are significanly affected by the deviatoric response of the matrix, thus largely simplifying the formulation of the viscoelastic constitutive behaviour at the composite scale. Analytical and numerical homogenisation procedures are used to evaluate the pertinence of the proposed model.