Strain rate sensitivity of rotating-square auxetic metamaterials

Abstract

This study provides an in-depth analysis of the mechanical behavior of rotating-square auxetic structures under various strain rates. The structures are fabricated using stereolithography additive manufacturing with a flexible resin. Mechanical tests performed on structures include quasi-static, intermediate, and high strain rate compression tests, supplemented by high-speed optical imaging and two-dimensional digital image correlation analyses. In quasi-static conditions (5 × 10^–3 s^-1), multiscale measurements reveal the correlation between local and global strains. It is shown that cell hinges play a significant role in structural deformation and load-bearing capacity. In drop tower impact conditions (intermediate strain rate of ca. 200 s^-1), the auxetic structures display significant strain rate hardening compared to loading at quasi-static rates. The thin-hinge structures maintain a Poisson's ratio of approximately -0.8, showing higher auxeticity than slow-rate compression tests. High strain rate conditions (ca. 2000s^-1) activate additional deformation mechanisms, including a delayed state of equilibrium exemplified by a heterogeneous distribution of lateral strains, possibly due to stress wave interactions and inertial stresses. The study further reveals nonlinear correlations between Poisson's ratio, strain, and strain rate, indicating reduced auxeticity at higher strain rates. These observations are discussed in terms of complex wave interactions and the strain rate hardening characteristics of the base polymer.