Designing staggered platelet composite structure with Gaussian process regression based Bayesian optimization

The staggered platelet composite structure, one of the most well-known examples of biomimetics, is inspired by the microstructure of nacre, where stiff mineral platelets are stacked with a small fraction of soft polymer in a brick-and-mortar style. Significant efforts have been made to establish a framework for designing a staggered platelet pattern that achieves an excellent balance of toughness and stiffness. However, because no analytical formula for accurately predicting its toughness is available because of the complexity of the failure mechanism of realistic composites, existing studies have investigated either idealized composites with simplified material properties or realistic composites designed by heuristics. In the present study, we propose a Bayesian optimization framework to design a staggered platelet structure that renders high toughness. Gaussian process regression (GPR) was adopted to model statistically the complex relationship between the shape of the staggered platelet array and the resultant toughness. The Markov chain Monte Carlo algorithm was used to determine the optimal kernel hyperparameter set for the GPR. Starting with 14 initial training data collected with uniaxial tensile tests, a GPR-based Bayesian optimization using the expected improvement (EI) acquisition function was carried out. As a result, it was possible to design a staggered platelet pattern with a toughness 11% higher than that of the best sample in the initial training set, and this improvement was achieved after only three iterations of our optimization cycle. As this optimization framework does not require any material theories and models, this process can be easily adapted and applied to various other material optimization problems based on a limited set of experiments or computational simulations.