FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design

Auxetic structures, known for their negative Poisson's ratio, exhibit effective elastic properties heavily influenced by their underlying geometry and base material properties. While periodic homogenization of auxetic unit cells can be used to investigate these properties, it is computationally expensive and limits design space exploration and inverse analysis. In this paper, the fast Fourier transform (FFT)-based homogenization approach is adopted to efficiently generate data for developing surrogate models, bypassing concerns about periodic mesh generation and boundary conditions typically associated with the finite element method (FEM). Surrogate models are developed for the real-time prediction of the effective elastic properties of auxetic unit cells with orthogonal voids of different shapes. The generated surrogate models accept geometric parameters and base material properties as inputs to predict the effective elastic constants in real-time. This rapid evaluation enables a practical inverse analysis framework for obtaining the optimal design parameters that yield the desired effective response. The performance of the generated surrogate models is rigorously examined through a train/test split methodology, a parametric study, and an inverse problem. Finally, a graphical user interface (GUI) is developed, offering real-time prediction of the effective tangent stiffness and performing inverse analysis to determine optimal geometric parameters. • FFT-based homogenization is employed to efficiently generate extensive datasets for auxetics, avoiding limitations of FEM. • Surrogate models are developed, enabling real-time prediction of elastic constants using geometric and material inputs. • A swift inverse design framework is established for flexible selection of effective elastic constants as desired outputs. • A user-friendly GUI is developed for real-time prediction and efficient inverse design.