An objective tensor to predict anisotropic fiber orientation in concentrated suspensions

The improved anisotropic rotary diffusion (iARD) model was previously regarded as a suitable description of anisotropic orientation states for long fibers in concentrated suspensions. However, the iARD tensor does not pass the classic rheological rule of Euclidean objectivity, namely, material frame indifference. It is hard to ignore the nonobjective effect due to the fact that different coordinate systems may yield different answers. Such an issue can be attributed to the iARD tensor related to the nonobjective velocity-gradient tensor. We therefore proposed a new iARD tensor, which depends on the square of the objective rate-of-deformation tensor. It is important to differentiate between the original Phelps–Tucker anisotropic rotary diffusion tensor and the objective iARD tensor via computing their first invariants. Furthermore, we validated this new iARD model's accuracy in predicting a distinct, broader core-shell orientation structure of injection-molded long-fiber composites through careful experimental verification.