Validation of a new viscoelastic model for unidirectional polymer matrix composites by analytical and numerical homogenisation

The long-term response of unidirectional, fibres-reinforced, polymer matrix composites is affected by the viscoelastic behaviour of the matrix. Most composite models introduce a different relaxation function for each of the five elastic parameters describing the transversely isotropic response at the scale of the homogenised ply, thus requiring long identification procedures based on multiple experimental tests. A new transversely isotropic model in the small strains regime was recently introduced by the authors, who used a Cartan decomposition in order to derive a new set of elastic parameters, which are more directly related to the behaviour of the underlying constituents. In particular, the deviatoric viscoelastic response of the matrix strongly affects only two of the five newly introduced parameters. In this work, analytical and numerical homogenisation approaches are developed and implemented in order to challenge such hypothesis and to validate the proposed model. In particular, a periodic homogenisation strategy enabling to impose general loading paths in terms of macroscopic strains and/or stresses on a Representative Volume Element (RVE) was developed in Abaqus, and used as a “virtual testing machine” to provide data to compare the transversely isotropic composite model proposed by the authors to the homogenised response of the RVE.