Material card’s identification by inverse method and multi-scale optimization approach through eigenmode analysis of unidirectional Elium®/flax laminated biocomposites

Abstract

This article presents a mixed finite element method (FEM) and experimental inverse identification approach for determining the ply-level elastic properties of unidirectional (UD) Elium®/flax composites. Using the global dynamic response of UD laminates, the intrinsic mechanical properties are identified. Material uncertainties are accounted for, and engineering constants are determined over a broad frequency range through a response surface methodology (RSM)-based sensitivity analysis and meta-modeling approach. A multi-objective optimization process based on a non-dominated sorting genetic algorithm (NSGA) is employed to minimize differences between experimental and numerical frequency responses. The sensitivity analysis reveals that the first seven vibration modes are primarily influenced by the longitudinal modulus (E₁) and the shear modulus (G₁₂), with E₁ having a dominant effect in UD configurations. The optimization process, conducted using HyperStudy™, demonstrates good agreement between the numerical and experimental frequencies. However, the use of a global error function reveals certain limitations, as it may fail to smooth out local deviations, making it challenging to precisely identify mismatches in individual vibration modes. In summary, these findings provide valuable insights into the dynamic behavior of Elium®/flax composites and offer a robust method for determining material properties card for future complex composite structures.