Reliable uncertainty quantification for fiber orientation in composite molding processes using multilevel polynomial surrogates

Fiber orientation is decisive for the mechanical performance of composite materials. During manufacturing, variations in material and process parameters can influence fiber orientation. We employ multilevel polynomial surrogates to model the propagation of uncertain material properties in the injection molding process. To ensure reliable uncertainty quantification, a key focus is deriving novel error bounds for statistical measures of a quantity of interest. Numerical experiments employ the Cross-WLF viscosity model and Hagen-Poiseuille flow to investigate the impact of uncertainties in fiber length and matrix temperature on the fractional anisotropy of fiber orientation. The Folgar-Tucker equation and the improved anisotropic rotary diffusion model, incorporating analytical solutions, are used for verification. Results show that the method improves significantly upon standard Monte Carlo estimation, while also providing error guarantees. These findings offer the first step toward a reliable and practical tool for optimizing fiber-reinforced polymer manufacturing processes in the future.