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Author ORCID Identifier
Open Access Dissertation
Doctor of Philosophy (PhD)
Year Degree Awarded
Month Degree Awarded
Statistical, Nonlinear, and Soft Matter Physics
The wrinkling and buckling of thin solids are common phenomena in our daily life and can be observed in many situations, such as crumpled papers, stretched plastics, compressed metals, clothes on our bodies and even furrowed human skin. Understanding of these phenomena has therefore long drawn interest of scholars. In this thesis, we discuss two buckling problems numerically and analytically. First, we study the wrinkling mechanism of stretched sheets with clamped edges. A central puzzle underlying this canonical example of “tensional wrinkling” has been the origin of compressive stress, which eventually leads to buckling instability. We elucidate the source of the compression as the relative extension of the clamped edge in comparison to the bulk of the sheet, and show how it gives rise to buckling instability. Distinguishing between a “near-threshold” parameter regime, in which the stress is well approximated by the planar, unwrinkled state, and a “far-from-threshold” regime, where wrinkles have a strong, non-perturbative effect, we address the transition of the morphology from a buckling-like to wrinkling-like pattern. Our work reveals that the stretch-induced wrinkling also arises from a common compressional confining geometry rather than from Poisson’s contraction as argued in previous research, thereby elucidating the conceptual similarity between this problem and other wrinkling problems. The second phenomenon we address is the emergence of defects and amplitude modulations in non-ideal patterns, where the locally-favorable wrinkle wavelength is inconsistent with the geometry imposed by confining forces. With such a problem, we seek to push the understanding of wrinkles from ideal cases to a case that is closer to natural situations. We propose a relatively simple theoretical model to study the wrinkling patterns in such a scenario. Finally, we include a technical chapter that elaborates on the numerous subtleties that must be taken into consideration by practitioners who seek to use the “Surface Evolver” algorithm for numerical simulations of elastic sheets, e.g. how to properly disable features designed for liquid surfaces, how to define the reference configuration and deal with refinements, and so on
Xin, Meng, "DEFORMATIONS OF GEOMETRICALLY FRUSTRATED ELASTIC SHEETS" (2023). Doctoral Dissertations. 2870.
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