An experimentally validated machine learning framework for efficient prediction of effective elastic properties of windmill-shaped auxetic structures

The article presents a numerical framework for evaluating the linearly elastic effective material properties of a recently developed two-dimensional windmill-shaped auxetic structure. The effective properties are obtained through homogenization of the representative volume element (RVE). Due to the complexity and inefficiency of analytical approaches, a numerical strategy based on the finite element method (FEM) is employed to determine the orthotropic elastic properties of this structure, characterized by its in-plane geometric symmetry. The geometry of this 2D auxetic structure is defined by three parameters: outer ligament length (L), inner ligament length (r), and ligament thickness (t). A scaling analysis demonstrates that the effective properties remain invariant under proportional geometric scaling; therefore, two input variables (ligament angle (θ) and thickness-to-inner-ligament ratio (t/r)) are adequate to determine the properties. Accordingly, finite element simulations are conducted on multiple distinct RVEs, and the generated dataset is utilized for an artificial neural network (ANN) with two input features, i.e., θ and t/r. The ANN model demonstrates excellent predictive capability, and experiments are also conducted to validate its predictions. Furthermore, parametric studies reveal that tuning the geometric parameters of this auxetic structure significantly improves its effective material properties, highlighting its strong potential for advanced engineering applications.