Experiment-driven simplification of Johnson-Champoux-Allard-Lafarge model for fibrous materialsa)

Widely used empirical and semi-phenomenological models lack practicality due to unstable predictions, which exhibit poor reproducibility, or reliance on numerous parameters that are not directly measurable. This paper presents an experiment-driven method to simplify the Johnson-Champoux-Allard-Lafarge (JCAL) model using a two-microphone impedance tube. Bayesian inference is applied to determine the non-acoustical parameters (i.e., tortuosity, airflow resistivity, viscous and thermal characteristic lengths, and static thermal permeability), and the regression method is used to correlate porosity with these non-acoustical parameters. The simplified JCAL model is validated against the original model and experimental results for acrylic, silk, and wool fibers. The simplified JCAL model shows good agreement with the original model for acrylic and wool fibers. Both models perform reliably for porosities between 92% and 98%, but show a mismatch with experimental data at 99% porosity, likely due to frame vibration effects. The poroelastic behavior leads to the original and simplified JCAL models failure for silk fiber. This experiment-driven simplification method reduces the JCAL model to a single parameter, porosity, which significantly enhances computational efficiency and enables faster predictions. It also enhances the model's applicability to optimization strategies, such as tuning design parameters for optimal sound absorption while minimizing thickness and mass.