Abstract
Metamaterials are composite materials with unique properties due to their microstructure. One type of metamaterial is auxetics, which have a negative Poisson's ratio, causing them to expand under load in directions perpendicular to the applied force. Examples of natural auxetics include pyrite, paper, and some polymers, but humans also create such materials, often using 3D printing.
This paper is devoted to the development of an inverse problem solving method for determining the geometric parameters of an auxetic metamaterial based on its mechanical properties using machine learning. The goal of this approach is to improve the design process of auxetic metamaterials and create materials with better mechanical properties.
Two auxetic structures are considered: "butterfly" and "square mesh". To evaluate the effective properties of the metamaterial, a direct problem based on the equations of solid mechanics was solved. The simulation was performed using the finite element method, and the calculation of effective mechanical properties was performed using the Fidesis Composite module. More than 25 thousand solutions of the direct problem were created to create a data set for training the machine learning model.
The developed machine learning model is capable of predicting the parameters of an auxetic metamaterial with given values of Young's moduli and Poisson's ratios. The quality of the model was checked using the SMAPE metric, which showed an average error of about 5%.