Relating local field fluctuations in composites with the sensitivity of their effective response to constitutive parameters: An identification framework for elastic and viscoelastic materials

In the study of composite materials, accurately characterizing the individual properties of constituents is essential but often challenging due to the possible unavailability of raw materials and the complexity of conducting microscale experiments. Inverse homogenization offers a compelling solution by enabling the extraction of microscale properties directly from macroscale experiments, despite being an ill-posed problem. This study focuses on identifying unknown constitutive parameters by minimizing a cost function that measures the discrepancy between actual composite response data and the predicted homogenized behaviour based on candidate parameters. To tackle these optimization problems, both first and second-order gradient-based minimization schemes are employed. This requires evaluating the sensitivity of a composite's effective response to its constitutive parameters, which is related to local fluctuations in solution fields of elementary cell problems. To so do, first and second-order derivatives of macroscopic stress and effective energy potential are obtained in a general setting, including nonlinear behaviours. Sensitivity maps are computed to gain local information within the representative volume element. The methodology involves repeatedly solving cell problems, efficiently achieved using FFT-based full-field simulations for periodic composites. It is implemented in two test cases involving fiber-reinforced composites to identify hard-to-measure parameters: elastic properties of fibers and viscoelastic properties of the matrix. The latter case uses the Laplace–Carson transform to extend the method to viscoelastic materials. The targeted constitutive properties are successfully identified, and sensitivity analyses assess the effects of uncertainties on the identified parameters. The study provides guidelines for using this sensitivity-based approach in relevant situations.