On the cyclic elastoplastic shakedown behavior of an auxetic metamaterial: An experimental, numerical, and analytical study

This article presents the first experimental, numerical, and analytical study of the elastoplastic shakedown response of an auxetic metamaterial structure that elucidates interactions between auxeticity and maximum shakedown loading capacity. The study aims to determine the safe elastoplastic shakedown limit of perforated auxetic aluminum sheet structures (AA5083-TO) with fixed void fraction (16.4%) under ambient cyclic asymmetric uniaxial loading conditions. The motivation is that shakedown-based designs can be used to expand the feasible design space under cyclic loading conditions compared to conventional yield-limited designs. Finite element analyses with calibrated hardening models are used to develop Bree load-interaction diagrams that are experimentally validated. It is found that shakedown occurs at stress levels up to almost four times the elastic limit of the structure for a fixed allowable equivalent strain level near three percent. This shakedown multiplier is also sensitive to the extent of auxeticity in the structure and a parametric study and analytical model are used to identify underlying mechanisms and a potential maximum condition.