Crystalline solids found in nature have rather monotonous mechanical properties. For most materials, only two parameters are necessary to characterize them—the Young’s Modulus and Poisson’s ratio—and inter-material variability comes primarily from the scales of these parameters. This monotony boils down to (1) the linear (spring-like) forces between atoms/molecules in the crystal and (2) the isotropic (random) orientation of different crystalline domains.

In theoretical work starting in my postdoc, we investigated how origami-based materials could break this monotony. The key idea is that by designing interesting geometries into the unit cell, one can control the macroscopic mechanical properties. Origami-based structures are interesting as an alternative because they are highly non-linear. First, the deformation energy in origami is concentrated in the folds, which behave as torsional springs—hence by definition not spatially linear. Second, constraints in the folding motions lead to geometric non-linearities. In our first important result published in Physical Review Letters (and with a follow up in PRE), we showed how these non-linearities lead to inherent mechanical multistability in origami-based crystals. The most recent result was in Nature Physics, where we (1) solved the puzzle of how to design patterns that meet the geometric constraints required for folding, and (2) showed how some of these patterns can be designed to fold into more than one target shape.

Many open questions remain. In particular, much of our theoretical work has yet to be seen in practice due to the difficulty of fabricating robust origami mechanisms. Future projects may venture into this territory.


Non-Euclidean Origami
Scott Waitukaitis, Peter Dieleman, and Martin van Hecke
accepted at Physical Review E

Jigsaw puzzle design of pluripotent origami
Peter Dieleman, Niek Vasmel, Scott Waitukaitis, and Martin van Hecke
Nature Physics, 16, 63-68 (2020).

Clicks for Doughnuts 
Scott Waitukaitis
Nature Physics 14, 777-778 (2018).

Origami building blocks: generic and special four vertices
Scott Waitukaitis and Martin van Hecke
Physical Review E 93, 023003 (2016).

Origami multistability:  from single vertices to metasheets
Scott Waitukaitis, Rémi Menaut, Bryan Chen and Martin van Hecke
Physical Review Letters 114, 055503 (2015).