Design optimisation of kirigami-based auxetic metamaterials with multistability and shape-morphing capability

This study presents the development of kirigami-based auxetic metamaterials with multistability and shape-morphing capabilities through a design optimisation framework leveraging machine learning technology. The framework employs surrogate models and a differential evolution algorithm to optimise the design variables of a kirigami cell, ensuring specified bistability and scalability conditions. This cell-level optimisation is extended to the structure-level, where each cell is optimised for its assigned multistability and scalability. For multistability, the auxetic structure is divided into subregions with distinct bistability levels, with optimisation conducted accordingly. For shape morphing, the expansion ratio of each cell is predefined according to the target geometry, with optimisation performed to ensure required scalability. Various auxetic structures, combining different bistability levels and target geometries, are optimally designed and additively manufactured for experimental validation. The experimental results confirm that the proposed design optimisation effectively controls the auxetic behaviour, enabling tunable shapes morphing and programmed transformation sequences.