Programming curvatures by unfolding of the triangular Resch pattern

The multi-degree of freedom Resch pattern forms most of its surfaces by tuning the folding angles of its creases. In this research, we program the triangular Resch pattern to naturally achieve surfaces with various curvatures by predefining the neutral angle and stiffness of the creases for the whole pattern. We simulate the free unfolding of tessellations by combining a bar-and-hinge model with an explicit meshless method, namely, the finite particle method. The effects of the damping factor, crease stiffness, and neutral angle on the unfolding process are investigated. The neutral angle of the creases plays a critical role in determining the final stable shape of the pattern. Then, we break the natural symmetry of the tessellations by changing the neutral angle and applying specific constraints to active creases to create stable unfolding surfaces with various curvatures. This study provides a foundation for the development of programmed curvatures of metamaterials that can be folded into origami patterns with multiple degrees of freedom.

Automated summary

This research explores the manipulation of folding angles in Resch patterns to achieve different surfaces, and investigates the impact of damping factor, crease stiffness, and neutral angle on the unfolding process. By changing the neutral angle and applying constraints, stable unfolding surfaces with various curvatures can be created.