  Non-rigid origami patterns could provide more versatile performance than
their rigid counterparts in the design of mechanical metamaterials owing to the
simultaneous deformation of facets and creases, but their complex deformation
modes make quantitative characterization and programmability of mechanical
properties a challenging task. Here, we investigated the tensile behavior of a
non-rigid square-twist origami structure with rotational symmetry by combining
biaxial tension experiments and finite element modeling. A three-stage
deformation process, including tightening, unlocking, and flattening, of the
structure was unveiled through a detailed analysis of facet distortion and
crease rotation, and the relationship between structure deformation and several
key features in the energy, force, and stiffness curve was obtained. Based on
the analysis, an empirical model was built to correlate the geometric and
material parameters of the structure and its deformation energy, initial peak
force, and maximum stiffness, which were further validated through experiments.
Using the model, the mechanical properties of the structure can be accurately
predicted and programmed based on specific engineering requirements, thereby
serving the development of new programmable mechanical metamaterials based on
the family of square-twist origami.
