The effect of fibre orientation closure approximations on mechanical property predictions

Current approaches used to simulate the flow of short-fibre suspensions employ fibre orientation tensors where the dependence upon higher-order orientation tensors is alleviated through the use of a closure. Unfortunately, the effect that a given closure has on material property predictions has received little attention in the literature. Accordingly this investigation demonstrates that current objective fourth-order closures assume an orthotropic form, whereas existing sixth-order closures are shown to provide a material representation with fewer symmetries than orthotropic. Numerical calculations demonstrate the existence of shear–extensional and shear–shear coupling in simple homogeneous flow and for a center-gated disk. Although these components are minor in comparison to principal components of the stiffness tensor, these components can be obtained via existing sixth-order closures.