PhD Thesis Defense: Xiaomin Han

Tuesday, March 26, 2019, 3:30–5:30pm

Rm. 118, Cummings Hall

“Mechanical self-assembly and multi-stability of thin structures”


Mechanical multi-stable structures have multiple distinct statically stable shapes and are commonly seen in nature and engineering, e.g. the open and closure of a flytrap. Mechanical multi-stabilities are traditionally perceived as a failure mechanism. However, actively employing instabilities in shape formation is commonplace. Thin structures comprise an increasing portion of engineering construction with areas of application becoming increasingly diverse. This study aims to comprehend the bi-stable and multi-stable behavior of thin structures with the intention of their utilization in engineering applications. The driving forces of multi-stable shape formation can be distributed either discretely or continuously over a thin shell, leading to varies forms of engineering constructions including origami, thin-walled plates, etc. The study focuses on understanding the effects of material properties and geometry variables theoretically and experimentally.

Firstly, we introduce an origami tessellation that resembles a helix of lined up, bistable diamond patterned units, and compare them with continuous helical ribbons. Paper-based helical origami can have almost infinitely many configurations by tuning the folding angles and exhibit bistability (i.e., having two different stable shapes given the same set of folding angles). We develop geometric relationships and energy functions to predict the equilibrium configuration and bi-stable behavior of such structures. Moreover, we construct two thick-panel versions of helical origami, one using a shape memory polymer to control the hinge angles and the other with torsional springs. Both structures exhibit bistability and can be triggered to snap into the other stable shape in response to heat or external forces. Secondly, 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. The 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. Thirdly, applications of multi-stable structures in robotics, wearable devices, and implantable devices are investigated. Controllability and responsiveness can be achieved by optically triggered shape transitions between two stable geometric configurations, which is actively employed to control the motion of a cardiac tissue engineered soft robot. Shape transitions between two stable states of piezoelectric materials generate remarkable and steady power output when subject to a periodic external mechanical force input, which has the potential capability to power the electronic devices and extends the battery lifetime.

Thesis Committee

For more information, contact Daryl Laware at