Dissertation/Thesis Abstract

Mechanical Self-Assembly and Multistability in Thin Structures
by Han, Xiaomin, Ph.D., Dartmouth College, 2019, 132; 13860612
Abstract (Summary)

Mechanical multi-stable structures have multiple distinct stable shapes and are commonly seen in natural and engineered systems, e.g. the open and closure of a flytrap. Mechanical multi-stability is traditionally perceived as a failure mechanism. However, actively employing instabilities in shape formation and transition 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 intent of utilizing them in engineering applications. The driving forces of multi-stable shape formation can be distributed either discretely or continuously over a thin shell, leading to various forms of engineering constructions including origami, thin-walled plates, bio-hybrid robots etc.

The study focuses on designing bistable/multistable structures that can be utilized in engineering and understanding the fundamental principles. 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. 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 folding angles and the other with torsional springs. With fixed rest angles, 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 theory 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. 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. Thirdly, applications of multi-stable structures in robotics are investigated. Periodic contraction of cells can be utilized to propel the motion of the bio-hybrid robot. 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. Last but not least, we design energy harvesters based on the bistable plates. Shape transitions between two stable states of piezoelectric materials generate remarkable voltage output when subject to a periodic external mechanical force input. Strain-engineering method is used to fabricate the bistable energy harvester and scalability study shows its potential capability to power the implantable electronic devices and extends the battery lifetime.

Indexing (document details)
Advisor: Chen, Zi
Commitee: Phan, Minh Q., Shan, Wanliang, Zhang, John X. J.
School: Dartmouth College
Department: Engineering
School Location: United States -- New Hampshire
Source: DAI-B 80/09(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Engineering, Mechanical engineering
Keywords: Mechanical self-assembly and multistability, Thin structures
Publication Number: 13860612
ISBN: 9781392117651
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