Integrating experiments, finite element analysis, and interpretable machine learning to evaluate the auxetic response of 3D printed re-entrant metamaterials

Metamaterials have received extensive attention in fundamental and applied research over the past two decades due to their unique mechanical behavior. This paper presents an interpretable machine learning (ML) approach for efficient response prediction of three-dimensional (3D)-printed metamaterials. However, developing such an ML-based model requires a large consistent, representative, balanced, and complete dataset. To this extent, an experimentally validated finite element analysis (FEA) approach is implemented to generate 8096 non-self-intersecting re-entrant honeycomb structures by varying the mesoscale geometrical features to obtain the corresponding Poisson's ratios. This dataset is leveraged to develop a feed-forward multilayer perceptron-based predictive model. The developed ML model shows excellent predictive efficacy on the unseen test dataset. Shapely additive explanation (SHAP) is then used for model interpretation. SHAP results show that the slant cell length is the dominant input feature dictating the model output whereas cell angle and vertical cell length show mixed trends signifying that other input features influence their effect on the model output. Moreover, cell thickness does not significantly influence the model output when compared to other input features. Overall, the integrated numerical simulation-experiment-interpretable ML-based predictive approach presented here can be leveraged to design and develop metamaterials for a wide range of engineering applications.