Self-assembly and Multistability of Thin Structures

Helical Origami, its multistability and self-deploying

Helices have been naturally selected for in nature, as they make economical use of space and feature good load-bearing capability. In recent years, origami structures have emerged as versatile building blocks and metamaterials with a variety of engineering applications due to their programmable deployability, multistability and tunable stiffness. Here we introduce an origami tessellation that resembles a helix of lined up, bistable diamond patterned units, and compare them with continuous helical ribbons. Paper constructed helical origami shows several representative configurations including two different types of helices. When constructed from nonpaper materials with hinges connected by shape memory polymer, it can respond predictably after it is heated, stretched, and then cooled by self-folding into a cylindrical or a twisted helix configuration. This controlled bistability and self-deployability can be adopted for deploying helical antennae in satellites, and in many other fields.

Spontaneous Curling of thin shells and their instabilities

Thin shell structures with spontaneous curvatures are ubiquitous in natural and synthetic systems, from curvy leaves to potato chips, from spring tapes to the Venus flytrap. However, the large deformation and instability phenomena of shells due to geometric nonlinearity, which often arise in morphogenesis and nanofabrications, remain highly nontrivial and a unified theory is lacking. Here we create spontaneously curved shapes with pre-strains and study their instabilities with a minimal theory based on geometrically nonlinear elasticity. Specifically, we propose a simple two-parameter linear elasticity model and identify a key dimensionless parameter associated with instabilities of the plate (“taco roll” and “potato chip” instability), validated by table-top experiments. A circular disc bends under homogeneous pre-strains with a non-zero Gauss curvature when the dimensionless parameter is small. When that parameter exceeds a certain threshold, however, the disc curves into a nearly developable shape and can bend along any direction equally likely (referred to as “taco roll” instability here). We give a rigorous derivation of the threshold value of the dimensionless parameter at which bifurcation occurs, and show that this model can also be employed to account for “potato chip” instability where bifurcation leads to bistable states that continuously and asymptotically transition into nearly cylindrical shapes bending along perpendicular directions. In fact, this dimensionless parameter governs not only in these in the “taco roll” and “potato chip” instability, and can be applied to study twisting of discs due to swelling and bistable morphing structures such as slap bracelets and the Venus flytrap. But unlike the geometric dimensionless parameter proposed by previous researchers, this new parameter does not involve the a priori unknown curvature. Moreover, this minimal theory is shown to be obtained from a “first-principle” derivation through elasticity theory and differential geometry, yielding predictions in excellent agreement with recent studies. Our work provides a simplified theoretical framework for large deformation of plates and shells with geometric incompatibility, and a unified picture for addressing different types of mechanical instabilities. This work will promote quantitative understanding of the morphogenesis of growing soft tissues, and meet the emergent needs of designing stretchable electronics, artificial muscles and bio-inspired robots.

Remotely Controlled Soft Robot

under construction/manuscript submitted

Bistable Piezoelectric Energy Harvesters and Helical Energy harvesters

Under Construction/ongoing research