Neural network‐based closure for modeling short‐fiber suspensions

Abstract Fiber orientation tensors enjoy widespread application in short‐fiber reinforced polymer composite simulations because they provide a compact form for describing complex fiber orientation states. The orientation of reinforcing fibers within a short‐fiber composite directly affects the mechanical and thermal properties of the processed part, requiring that an accurate and efficient simulation method be available for use in product and process design. It is well understood that the equation of motion for each even‐ordered orientation tensor is dependent on the next higher even‐ordered orientation tensor, necessitating the use of a closure approximation. This article presents a new class of fitted orientation tensor closures where components of the fourth‐order tensor are computed from corresponding second‐order tensors using an artificial neural network (ANN). The ANN offers a unique advantage here because it is computationally efficient and is able to represent complex relationships between inputs and outputs where representative mathematical models do not exist. After a brief review of fiber orientation analysis, the new neural network closure (NNET) is defined along with a detailed description of the associated training procedure. The accuracy and computational efficiency of the NNET closure is then demonstrated with both simple and complex flow simulations.It is shown that simulations with the new NNET closure are as accurate as those using current orthotropic fitted closures at a computation cost that approaches the less accurate Hybrid closure. POLYM. COMPOS., 31:1125–1141, 2010. © 2009 Society of Plastics Engineers