LAUSR

Purpose The orientation behavior of fiber is of great significance in improving the performance of fiber-reinforced polymer products. Generally, the Folgar–Tucker equation can accurately describe the variation of orientation vector of fiber, whereas the stability of numerical algorithms was the major challenge. This paper aims to propose an accurate, stable algorithm to solve the Folgar–Tucker equation for the fiber orientation behavior. Design/methodology/approach First, the mismatch problem between the strain rate and the pressure field was solved by using the integral transformation method. Then, an accurate, stable algorithm to solve the Folgar–Tucker equation based on the invariant-based optimal fitting method was proposed. The equation was discretized by finite element/finite difference method, and the Lagrange multiplier method was applied to ensure stability. Findings The proposed algorithm is proven to accurately and steadily coincide with the experimental results for different cases, including the fiber orientation behaviors under combined flow field, rectangular sheet, three-dimensional computed tomography imaging of tensile specimen and box cases. Originality/value The fiber orientation behavior during the injection molding can be accurately predicted, which plays a significant role in determining the mechanical properties of products.