On the isotropy of randomly generated representative volume elements for fiber-reinforced elastomers

The isotropy of different numerical simulations of fiber reinforced elastomers has been explored by explicitly applying stretch in different loading directions, in models with representative volume elements (RVEs) spanning a wide range of fiber volume fractions and system sizes. The results show that the homogenized response is not the same for all loading directions, and that the corresponding dependance takes the form of a sine. The anisotropy decreases with the RVE size, and so it can be used to asses if the scales can be separated in a given model. Considering the average response over all loading directions greatly reduces the variation between different RVEs, which can be used to improve the accuracy of the simulations in a way that is significantly more efficient than increasing the size of the RVE. The simulations have also shown a good correlation between the isotropy of each representative volume element at low and high values of the applied stretch. The result of linear simulations can therefore be used as an efficient indication of the anisotropy expected at high deformations.