Predicting the elastic modulus of fibrous networks: A micromechanical scaling approach

This study presents a micromechanical scaling approach to predict the Young's modulus of synthetic fibrous networks, such as polyester and polyethylene terephthalate. Using a customized experimental apparatus, relaxation tests were performed on various fiber types and carded blends across a density range of 70 to 180 kg/m3. A rigorous "shakedown" conditioning protocol was implemented to stabilize stochastic friction and isolate the purely visco-elastic response. Results indicate that the elastic modulus follows a power-law dependency on density. A semi-empirical model is proposed that explicitly decouples the effects of relative density and fiber radius, the latter determined through airflow resistivity measurements. The framework was successfully extended to multi-component fiber blends using equivalent macroscopic parameters. Validation through two-dimensional axisymmetric finite-element method simulations and normal incidence acoustic transmission loss measurements confirms the model's satisfying predictive reliability. This multi-scale approach provides a robust tool for the design and optimization of complex non-woven assemblies in thermo-acoustic and industrial applications.