Eigenmode-based inverse identification and multi-parameter sensitivity analysis of flax/Elium® laminates from unidirectional to cross-ply configurations validation

This article presents an extended validation of a previously developed inverse identification method, initially applied to unidirectional (UD) flax/Elium® laminates. The study aims to (i) confirm the robustness of the ply-level inverse approach under more complex cross-ply configurations and (ii) identify the dominant mechanical parameters influencing the vibration behavior of biocomposites beyond UD layouts. A comprehensive sensitivity analysis is conducted to assess the influence of material and geometrical parameters on the first seven vibration modes. While E1 and G12 predominantly govern the dynamic response in UD laminates, cross-ply configurations reveal additional influences from the transverse modulus E2 and interlaminar shear modulus G13. Enhanced coupling effects involving G12 are also observed. Structural variability is considered through parameters such as thickness and density, which reflect the heterogeneous nature of bio-based materials. A compensation mechanism is highlighted: increased thickness raises stiffness but also adds mass, partially offsetting frequency gains. The study demonstrates a progressive transition in dominant mechanical parameters across modes: lower modes (f1, f2) are controlled by E1, while higher modes become increasingly sensitive to G12, G13, and, to a lesser extent, E2. The proposed inverse method shows excellent agreement between simulated and experimental modal responses for both 4-ply and 8-ply laminates. The genetic algorithm converges toward realistic values—thickness between 3,03 mm and 3,17 mm and density around 1292 kg/m³—confirming the robustness of the approach. By accounting for both material variability and process-induced dispersion, the method contributes to more reliable modeling and optimized design of natural fiber composites.