Snap-through is a striking instability in which an elastic object rapidly jumps from one state to another. It is seen in the leaves of the Venus flytrap plant and umbrellas flipping on a windy day among many other examples. Similar structures that snap-through are used to generate fast motions in soft robotics, switches in micro-scale electronics and artificial heart valves. Despite the ubiquity of snap-through in nature and engineering, its dynamics is usually only understood qualitatively. In this thesis we develop analytical understanding of this dynamics, focussing on how the mathematical structure underlying the snap-through transition controls the timescale of instability. We begin by considering the dynamics of 'pull-in' instabilities in microelectromechanical systems (MEMS) - a type of snap-through caused by electrostatic forces in which the motions are dominated by fluid damping. Using a lumped-parameter model, we show that the observed time delay near the pull-in transition is a type of critical slowing down - a so-called 'bottleneck' due to the 'ghost' of a saddle-node bifurcation. We obtain a scaling law describing this slowing down, and, in the process, unify a large range of experiments and simulations that exhibit delay phenomena during pull-in. We also investigate the pull-in dynamics of MEMS microbeams, extending the lumped-parameter approach to incorporate the details of the beam geometry. This provides a model system in which to understand snap-through of a continuous elastic structure due to external loading. We develop a perturbation method that systematically exploits the proximity to pull-in to reduce the governing equations to a simpler evolution equation, with a structure that highlights the saddle-node bifurcation. This allows us to analyse the bottleneck dynamics in detail, which we compare with previous experimental and numerical data. The remainder of the thesis is concerned with the dynamics of snap-through in macroscopic systems. In particular, we explore the extent to which dissipation is required to explain anomalously slow snap-through. Considering an elastic arch as an archetype of a snapping system, we use the perturbation method developed earlier to show that two bottleneck regimes are possible, depending delicately on the relative importance of external damping. In particular, we show that critical slowing down occurs even in the absence of damping, leading to a new scaling law for the snap-through time that is confirmed by elastica simulations and experiments. In many real systems material viscoelasticity is present to some degree. Finally, we examine how this influences the snap-through dynamics of a simple truss-like structure. We present a regime diagram that characterises when the timescale of snap-through is controlled by viscous, elastic or viscoelastic effects.

The focus of the current research is to investigate the potential of using bistable unsymmetric cross-ply laminated composites as a means for achieving structures with morphed characteristics. To this end, an investigation of the design space for laminated composites exhibiting bistable behavior is undertaken and the key parameters controlling their behavior are identified. For this purpose a nonlinear Finite Element methodology using ABAQUS code is developed to predict both the cured shapes and the stability characteristics of unsymmetric cross-ply laminates. In addition, an experimental program is developed to validate the analytically predicted results through comparison with test data. A new method is proposed for attaching piezoelectric actuators to a bistable panel in order to preserve its favorable stability characteristics as well as optimizing the actuators performance. The developed nonlinear FE methodology is extended to predict the actuation requirements of bistable panels. Actuator requirements, predicted using the nonlinear FE analysis, are found to be in agreement with the test results. The current research also explores the potential for implementing bistable panels for Uninhabited Aerial Vehicle (UAV) wing configuration. To this end, a set of bistable panels is manufactured by combining symmetric and unsymmetric balanced and unbalanced stacking sequence and their stability characteristics are predicted. A preliminary analysis of the aerodynamic characteristics of the manufactured panels is carried out and the aerodynamic benefits of manufactured bistable panel are noted.

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<p>The main goal of this thesis research is to expand the range of unique properties of phase transforming cellular materials (PXCMs), a new class of architected materials, and to extend their applicability both in the engineering disciplines and in the medical field. A novel aspect of PXCMs is their unique energy dissipation during loading via a snapping mechanism associated with a geometric transition between one stable configuration to another stable configuration at the unit cell level. Phase transformation is analogous to displacive transformations, such as martensitic transformations in shape memory alloys, with no change in configurational entropy. To accomplish this goal, three problem areas are addressed with the first exploring the effects of length scale as added structural hierarchy on material properties and energy dissipation, the second providing an analysis of the durability of architected materials via a novel additive manufacturing method, and the third, an extension into the medical field. Two examples are provided that demonstrate the effects of length scale as added structural hierarchy on material properties, and a machine learning approach for the feasible design of materials with additional levels of structural hierarchy is presented. A simple design approach coupled with a novel additive manufacturing method is discussed for the design of architected materials with high durability. Lastly, a concept for de-clogging bile stents via a temperature driven, shape-memory mechanism inspired by peristaltic locomotion in the human esophagus is presented.</p>