A combined approach of experimental testing and inverse FE modelling for determining homogenized elastic properties of membranes and plates

Accurately determining the mechanical properties of complex materials is a key challenge in structural analysis, especially when using the finite element method (FEM). While homogeneous materials can be modeled with relative ease, heterogeneous materials such as composites or biological tissues with multiphase compositions pose significant difficulties due to the variability in their internal structures. The most used approach is numerical homogenization, which allows for the estimation of effective material properties by combining the characteristics of individual phases; however, this technique may not always be feasible, especially for materials with irregular or unknown phase distributions. This paper proposes an original methodology that combines non-destructive experimental testing with an inverse finite element modeling to extract the anisotropic elastic properties of quasi two-dimensional structures such as membranes and plates. The method involves modeling the component using membrane or plate finite elements, but managing a global stiffness matrix expressed analytically. While geometric information is incorporated in the global stiffness matrix, the material properties, specifically the components of the anisotropic elasticity matrix, remain unknown. The experimental data, comprising force and displacement measurements, are used to solve a nonlinear system, allowing for the identification of the material’s constitutive properties via numerical computation. To validate this approach, two experimental setups were conducted. The first involved a hyperelastic neoprene membrane, subjected to various biaxial preloading conditions, while the second focused on PLA plates produced through additive manufacturing including both homogeneous and reinforced variants. In both cases, the method successfully captured the full anisotropic elastic response, yielding accurate estimates of Young’s moduli, Poisson’s ratios, shear modulus, and orthotropy system orientation, in agreement with independent mechanical tests. This combined approach offers a practical and efficient solution for determining the elastic properties of complex materials, particularly in cases where traditional homogenization techniques are impractical or inadequate. Furthermore, this method can be a versatile tool for evaluating the damaging and aging effects on materials subjected to cyclic loading or those with irregular and complex internal structures.