Z. Javanbakht, W. Hall, A. Öchsner

• Herein, the general constitutive equation of bi-phasic materials equipped with orientation tensor is presented in direct notation. The formulation is refined by some correction factors specific to natural fibre-reinforced composites; then, a planar case is derived. The necessity of local information is emphasised through the introduction of auxiliary maps, which included volume fraction and orientation data. A semi-analytical homogenisation method is introduced through finite element analysis. Auxiliary maps are shown to be a better alternative to the overall orientation of fibres. Global calculations are insensitive to local variations whilst appropriate auxiliary maps offer refined results. Considering the multidisciplinary application of orientation tensors, the proposed scheme can be used in all areas where local information cannot be disregarded.