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

Abstract

Auxetic metamaterials (AM) with negative Poisson’s ratio (NPR) offer promising mechanical properties but often suffer from significant stress concentrations, compromising durability and fatigue life. Conventional design approaches, including topology optimization and empirical geometry-based methods, struggle with exploring complex design spaces, while data-driven techniques demand extensive datasets, making fatigue life prediction computationally expensive. To address these challenges, we propose a novel framework that integrates Bézier curve-based geometric parameterization, multi-objective Bayesian optimization (MBO), and fatigue life prediction via elastoplastic homogenization and critical distance theory. This approach systematically explores the design space, simultaneously enhancing NPR and optimizing fatigue resistance while alleviating localized stress concentrations. MBO efficiently balances exploration and exploitation with limited data, making it particularly suitable for computationally intensive fatigue analysis. Optimized AM structures exhibited an 85.11% increase in NPR and a 12.07% improvement in low-cycle fatigue (LCF) life compared to initial designs. Experimental validation confirmed up to 30 times the LCF life and a 2.5-fold NPR increase over conventional AM structures. These findings establish a scalable methodology for AM design, advancing the development of durable, high-performance metamaterials for biomedical, aerospace, and energy-harvesting applications.