Design of auxetic metamaterial for enhanced low cycle fatigue life and negative Poisson’s ratio through multi-objective Bayesian optimization

Auxetic materials (AM), characterized by their unique negative Poisson's ratio (NPR), are promising candidates for engineering applications such as piezoelectric energy harvesting and biomedical devices; however, achieving high NPR often leads to significant stress concentrations and limited durability. This study addresses these challenges by optimizing AM designs to reduce stress concentrations and enhance fatigue resistance while maintaining NPR. We propose a novel design methodology employing smooth Bézier curves, optimized along the Pareto front of NPR and low-cycle fatigue (LCF) life through critical distance theory, elastoplastic homogenization, finite element analysis (FEA), and multi-objective Bayesian optimization (MBO). The optimized designs achieved an 85.11% increase in NPR and a 12.07% improvement in LCF life compared to initial, randomly generated Bézier curve-based designs. Experimental validation using Al7075-T651 specimens showed that these optimized designs outperformed conventional AM structures, achieving up to 30 times the LCF life and a 2.5-fold increase in NPR. Our simulations also show that the optimized design can enhance piezoelectric energy harvesting, achieving a 228.89% increase in energy output. This adaptable framework for three-dimensional structures significantly enhances the potential of AM for advanced metamaterial applications with unique mechanical properties.