Sequential kriging-based closure approximations for flow-induced fiber orientation and prediction of composite stiffness

Orientation tensor has been widely applied to predict the orientation state of the fibers in injection molding simulations. Unfortunately, calculating the second-order orientation tensor needs to know the four-order orientation tensor, thus requiring a closure approximation. Developing an efficient and accurate closure has been a challenging subject. This article develops a sequential Kriging-based closure (KRI) approximation. We constructed the Kriging approximation of fourth-order orientation tensor in terms of the second-order orientation tensor. The maximization of expected improvement adds the second-order orientation tensors to improve the accuracy of the closure. Results demonstrate that the prediction of the KRI closure to accurately predict fiber orientation and fiber-reinforced composites stiffness is more accurate than the Hybrid, Orthotropic, and Natural closure for majority of the flows in industrial manufacturing processes. POLYM. COMPOS., 40:1748-1761, 2019. (c) 2018 Society of Plastics Engineers