Design of extremal reentrant auxetics using optimization algorithms

Abstract

A comprehensive understanding of the optimal achievable ranges of their key mechanical properties and the tradeoffs that govern them, which is foundational for the targeted design of multifunctional, performance-optimized lattices, remains elusive. The purpose of this study is to address this gap for 2D reentrant auxetic lattices using a systematic optimization framework, investigating the effects of the unit-cell geometric parameters (reentrant angle, height, width, strut length, and wall thickness) on the mechanical performance of these structures. Optimization was performed using both gradient-based methods (fmincon in MATLAB and Gekko in Python) and a population-based genetic algorithm (GA) to identify optimal unit cell configurations, map the design-space boundaries, and reveal critical multi-objective tradeoffs. The influence of the aspect ratio (H/W) on the achievable property ranges was systematically examined. Finite element simulations and quasi-static compression tests on 3D-printed PLA prototypes confirmed the theoretical predictions, with deviations of less than 10%. Key findings reveal that wider unit cells (low H/W ratio) increase longitudinal stiffness but reduce the attainable range of Poisson’s ratios, and vice versa. Structures attained negative Poisson’s ratios as low as −35.5, and the framework identified configurations with specific energy-absorption capacities up to approximately 32 times those of the base material.