Stability of highly nonlinear structures: snapping shells and elastogranular columns
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Highly nonlinear structures exhibit complex responses to external loads, and often become unstable. In this thesis, I consider structures with either a nonlinear geometric response or material response. Geometrically nonlinear bistable shells have two stable configurations and can reversibly change between them via snap-through instabilities. This snap-through behavior can cause large geometric deformations in response to small changes in loading, and thus is ideal for designing various devices. For materially nonlinear structures, one recent focus is the potential to utilize granular jamming to construct structures. However, it is not yet fully understood how the stability of such nonlinear structures is governed by geometric and materials properties. This thesis aims to answer this question and propose design guidelines for engineering applications. This research will focus on the statics and dynamics of spherical shells, prestressed bistable shells and elastogranular columns. For spherical shells, we aim to find out under what geometric criteria can a shell be turned inside out, and as the shell goes through the snap-through instability, what dictates the shape and speed of it. Geometric criteria to predict whether a spherical shell is bistable or monostable is proposed based on precisely fabricated soft spherical shells. Point load indentation tests were performed to determine how stable a spherical shell is in its everted configuration. The results show a distinct difference between shallow shells and deep shells, which led to further studies on the snapping dynamics of spherical shells. High speed videos are recorded to track the motion of the apex of an everted spherical shell during its snap-through process, and we find that as the spherical shell goes from shallow to deep, the axisymmetric snapping will transform into asymmetric snapping. This change in snapping modes greatly affects the snapping dynamics of the everted spherical shells, and the shapes they adopt through the instability. Besides spherical shells, we also analyzed prestressed, bistable, cylindrical shells. Prestressed bistable shells fabricated by stretching and bonding multiple layers of elastomers can have various geometric shapes and can snap under external stimuli, but the governing parameters for the fabrication and snapping are not known yet. An analytical model was proposed based on non-Euclidean Plate Theory to predict the mean curvature of the prestressed shell, and the amount of stimulus that is needed to trigger the snapping. Numerical simulations are performed to compare with the analytical results. Based on the proposed theory, for given fabrication parameters and material properties, the final mean curvature of the bistable prestressed shell can be predicted accurately, as well as the amount of stretch that is needed to trigger snapping. This study can be used to design smart actuators or other soft, smart devices. To study material nonlinear structures, we use a mixture of grains and rods to enable the formation of stable structures via granular jamming. Understanding how these constituents govern the mechanical properties of the jammed structures is crucial for devising relevant engineering designs. We examine freestanding columns composed of rocks and string, and propose a simple physical model to explain the resulting structure’s mechanical behavior. The results indicate that exterior fiber mainly contributes to stiffness, while interior fiber increases the stored elastic energy and absorbed total energy of the structures under certain external load. By assembling the grains and strings in an engineer way, structures with robust mechanical properties can be formed. The results provide guidelines that allow the design of jammed elastogranular structures with desired mechanical properties. The research results of this thesis will open and guide a variety of possibilities in designing functional responsive devices or jamming structures.