A theory for concentrated fiber suspensions with strong fiber‐fiber interactions

A theory is presented for the flow‐induced fiber orientation and stress in fiber‐reinforced polymer composites with planar fiber orientation. The rate of change of fiber orientation is given as a function of the strain rate in the continuum and the probabilistic effects of physical inter‐fiber contacts. The continuum stress is calculated from the stress in the fluid and fibers, where fiber stress is a result of the local disturbance in the fluid velocity field and of the inter‐fiber contact forces. Fiber orientation is described via a probability density function whose transport equation has the form of a standard advection‐diffusion equation with an orientation‐dependent rotary diffusion. This equation is solved using a finite difference scheme and the results are presented.