A stiffness programming framework for nonlinear hybrid Kresling – Yoshimura origami metastructures

Recent advancements in precise control and vibration suppression devices have created a growing demand for programmable mechanical elements. Although various origami structures have been introduced as potential candidates for this purpose, tailoring their stiffness behavior remains a significant challenge. To this end, this paper presents a systematic framework to assist in programming stiffness curves of nonlinear Kresling-Yoshimura hybrid cells under specific stiffness behaviors and geometric constraints. The framework explores all feasible combinations of geometric and mechanical parameters that contribute to the restoring force of such cells, including member lengths, diameters, and distinct shape ratios. Finite element analysis is employed to provide a practical tool to evaluate the nonlinear stiffness curves, which can be represented by cubic polynomials. Restoring force relationships are derived to ensure full recovery to the initial geometry, avoiding plastic deformation. Then, the effect of the main geometrical parameters on the linear and nonlinear stiffness coefficients is analyzed, providing a practical tool for designing the stiffness curve. The proposed hybrid cells demonstrate a high elastic deflection range, and a wide spectrum of linear and nonlinear stiffness behaviors. Comprehensive analysis proves that these hybrid origami structures hold significant promise for future implementation, with the potential to expand their operational range and accommodate diverse requirements in programmable stiffness applications.