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Abstract
Thin sheets are present in all areas of life, biologically relevant in various systems and scales from cell membranes to multi-layered tissues. Though compositionally very different, soft matter thin sheets all respond to imposed strains through deformation and mechanical instability. The type of resultant deformation and instability is dictated by the competing energetic costs of in-plane and out-of-plane deformation. The relative energetic costs of these two deformation modes are highly dependent on properties of the thin sheet such as material behavior, thickness, and geometric constraints. While existing theoretical models for thin sheet instabilities assume classic elasticity, infinitely thin sheets, and inextensibility, these assumptions often lack the complexity needed to capture the observed behavior of biological thin sheets. Utilizing continuum solid mechanics and elasticity, this dissertation probes the effects of adaptive material behavior, physically relevant thicknesses, and surgically motivated geometric constraints on emergent thin sheet mechanical deformations and instabilities. This work employs finite element simulations to model the mechanical response of biological thin sheets undergoing external loading and geometric manipulation, with the ultimate goal of developing, questioning, and building upon theoretical and computational frameworks of thin sheet mechanical response.