Multi-stability and variable stiffness of cellular solids designed based on origami patterns

Abstract

The application of origami-inspired designs to engineered structures and materials has been a subject of much research efforts. These structures and materials, whose mechanical properties are directly related to the geometry of folding, are capable of achieving a host of unique adaptive functions. In this study, we investigate a three-dimensional multistability and variable stiffness function of a cellular solid based on the Miura-Ori folding pattern. The unit cell of such a solid, consisting of two stacked Miura-Ori sheets, can be elastically bistable due to the nonlinear relationship between rigid-folding deformation and crease material bending. Such a bistability possesses an unorthodox property: the critical, unstable configuration lies on the same side of two stable ones, so that two different force-deformation curves co-exist within the same range of deformation. By exploiting such unique stability properties, we can achieve a programmable stiffness change between the two elastically stable states, and the stiffness differences can be prescribed by tailoring the crease patterns of the cell. This paper presents a comprehensive parametric study revealing the correlations between such variable stiffness and various design parameters. The unique properties stemming from the bistability and design of such a unit cell can be advanced further by assembling them into a solid which can be capable of shape morphing and programmable mechanical properties.