Curved-creased origami mechanical metamaterials with programmable stabilities and stiffnesses

Curved Crease Origami (CCO) structures exhibit intrinsic elastic behavior, resulting from a combination of crease folding and facet bending. In this work, we introduce a generic theoretical framework for constructing and predicting the mechanical properties of OMMs composed of curved crease unit cells, and an inverse design method that could achieve programmable stiffness and stability of CCO metamaterials, the CCO stacked unit with 2n-stability is first designed. Theoretical models, which could predict the in- and out-of-plane Poisson's ratios, uniaxial forces and stiffnesses of a single CCO tessellation, are constructed and validated by comparing with the finite element numerical method and experiment. Based on the analytical framework, the mechanical properties of the proposed CCO metamaterial with different crucial parameters are investigated, the results show that the combination of the initial folding angle pair could prominently affects the presence of bistability of the CCO unit. Our framework reveals that stacking two distinct layers of CCO units enables unique properties, such as bistability and zero stiffness, expanding the design space for CCO metamaterials. To determine the most suitable parameters for the unit cell to achieve programmable stabilities and targeted stiffness, the genetic algorithm is employed to optimize the basic model parameters and to carry out the inverse design, several case studies are demonstrated to show that the bistability model with specific stiffness, assigned stable locations, zero-stiffness in stable states and multistability model could be achieved. In summary, this work presents a comprehensive framework for designing and analyzing the curved crease origami mechanical metamaterials and proposes the inverse design method that could pave the way for a range of novel applications.