Multiscale wave-based identification of layer-specific geometric and viscoelastic parameters in heterogeneous multilayer composites using full-field measurements

The full model parameters estimation of heterogeneous multilayer composites (HMC), involving geometric parameters and static-dynamic viscoelastic properties, has attracted considerable attention for both damage diagnosis and the design of new materials. However, this remains a challenge in current research due to the complexity involved in identifying special layers. To this end, we developed a robust wave-based method to estimate the structural parameters of each layer in HMCs using full-field displacement data. The method follows a two-stage inversion process. In Stage I, it estimates geometric and elastic parameters, and in Stage II, it determines damping properties. These parameters can be static, dynamic, linear, nonlinear, or mixed. The objective is to optimize the identification process by combining the multi-scale wave and energy propagation modeling and characterization numerical methodology that automatically incorporates the limited knowledge on both the used predicted Finite Element model (whatever its complexity) and experimental data (inevitably noisy). The Condensed Wave Finite Element Method with Contour Integral solver (CWFEM-CI) is proposed to model wave and energy propagation in mesoscopic predicted models by solving a nonlinear eigenvalue problem. It enables complex wavenumber extraction in arbitrary directions while reducing computational cost through model order reduction approach, Component Mode Synthesis (CMS). At the macroscopic scale, Algebraic K-Space Identification 2D (AKSI 2D) is applied to retrieve complex wavenumbers from real materials, serving as reference data for inverse optimization. By embedding iterated integrals into the mathematical foundation of the method, signal noise is effectively suppressed, thereby ensuring accurate material identification. Finally, the identification problem is formulated and solved iteratively using the surrogate optimizer, which minimizes the difference between predicted and experimental wave propagation parameters. The accuracy and effectiveness of the proposed method are validated through numerical experiments on linear elastic, nonlinear viscoelastic, and heterogeneous multilayer models, using both synthetic and real full-field data.