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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01rv042t09s
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dc.contributor.advisorHaataja, Mikko P.en_US
dc.contributor.advisorSrolovitz, David J.en_US
dc.contributor.authorChen, Zien_US
dc.contributor.otherMechanical and Aerospace Engineering Departmenten_US
dc.date.accessioned2012-03-29T18:05:01Z-
dc.date.available2014-02-03T07:00:19Z-
dc.date.issued2012en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01rv042t09s-
dc.description.abstractMechanical forces play a key role in the shaping of versatile morphologies of thin structures in natural and synthetic systems. The study of large deformation and instability of thin objects will facilitate understanding of morphology generation in these systems, and benefit the ongoing efforts in developing programmable microfabrication techniques and novel functional devices including artificial muscles, stretchable electronics and bio-inspired robots. For this purpose, in this thesis, the morphology and deformation of thin ribbons, plates and rods and their instabilities are systematically investigated, through both theoretical modeling and table-top experiments. First, a theoretical model based on linear elasticity theory, differential geometry and stationarity principles is developed for the spontaneous bending and twisting of ribbons with tunable geometries in presence of mechanical anisotropy. It is shown that helicity arises from mechanical anisotropy and the mis-orientation between the principal axes of effective surface stresses and geometric axes of the ribbon. Closed form analytic predictions are obtained from this theory with no adjustable parameters, and validated with simple, table-top experiments that are in excellent agreement with the theoretical predictions. Since the ribbon bends in two directions with non-zero Gauss curvature, this approach for thin, narrow ribbons goes beyond the scope of the classical Stoney formulation of planar bending of ribbons under surface stress. For large deformation of ribbons and plates, a more general theory is developed to account for mechanical instability induced by geometric nonlinearity, due to the competition between inhomogeneous bending and mid-plane stretching energy. This comprehensive, reduced parameter model leads to unique predictions that are validated with a series of table-top experiments. Moreover, it is shown that edge effects can alter the energy profile of the two locally stable states when the in-plane dimensions are asymmetric (i.e., when the length does not equal the width). Yet another related topic, large deformation and instability of rods, is also addressed in this thesis. A model is proposed to investigate buckling behavior of rods embedded in an elastic medium and in the presence of external torques applied at the two ends. Such a study is relevant for instability-related phenomena in a broad spectrum of natural and synthetic systems, including helical growth of plant roots, buckling of cytoskeletal tissues and mechanotransduction in cells, and helical buckling of oil pipes in wellbores. This thesis complements the reviving efforts in studying mechanics and geometry of thin objects, and will promote understanding of morphology and pattern formations in a variety of natural and engineered systems, and meet the emergent needs for developing programmable micro-/nano-fabrication techniques and designing bioinspired devices with smart, functional responses to external stimuli.en_US
dc.language.isoenen_US
dc.publisherPrinceton, NJ : Princeton Universityen_US
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the <a href=http://catalog.princeton.edu> library's main catalog </a>en_US
dc.subjectbistabilityen_US
dc.subjectbucklingen_US
dc.subjecthelicesen_US
dc.subjectlayered materialsen_US
dc.subjectshells and membranesen_US
dc.subjectsurface stressen_US
dc.subject.classificationMechanical engineeringen_US
dc.subject.classificationMaterials Scienceen_US
dc.subject.classificationMechanicsen_US
dc.titleNonlinear Mechanics, Morphology and Instability of Ribbons, Plates and Rodsen_US
dc.typeAcademic dissertations (Ph.D.)en_US
pu.projectgrantnumber690-2143en_US
pu.embargo.terms2013-12-27-
Appears in Collections:Mechanical and Aerospace Engineering

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