Library

eCommons

 

SPATIAL LOCALIZATION IN NONLINEAR ELASTICITY VIA GLOBAL BIFURCATION

Simple item page
dc.contributor.authorPandurangi, Shrinidhi Shrikant
dc.contributor.chairHealey, Timothy James
dc.contributor.committeeMemberHui, Chung Yuen
dc.contributor.committeeMemberRand, Richard Herbert
dc.contributor.committeeMemberTriantafyllidis, Nicolas
dc.contributor.committeeMemberElliott, Ryan S.
dc.date.accessioned2021-03-12T17:40:47Z
dc.date.available2022-08-27T06:00:22Z
dc.date.issued2020-08
dc.description163 pages
dc.description.abstractIn this dissertation, we study spatially localized pattern formations in highly deformable solids that can be characterized by their nonlinear elastic behavior. Three distinct problems are considered in this work: localized wrinkling of long beams resting on softening foundation, folding of beams on foundations and surface creasing in solids. In the context of localized wrinkling, we discuss a phenomenon associated with hidden symmetry that emerges asymptotically in finitely long beams on foundations, a problem having a finite symmetry group, when a certain non-dimensional length becomes very large. Later in this work, we study highly localized deformations that appear in the form of fold patterns in beams on elastic foundations and self-contacting surface creases on soft solids subjected to compression. We propose a robust computational methodology which is based on using bifurcation theory coupled with efficient numerical continuation techniques to compute such deformations. We make use of inherent symmetry in the system to work with appropriately chosen constraints and compute different symmetry-breaking bifurcation paths and study the stability of solutions on these paths. In particular, we show that folding and creasing are not local bifurcations from the state of homogeneous deformations of beams and solids respectively. They rather emerge as nonlinear deformations that evolve along global bifurcation paths.
dc.identifier.doihttps://doi.org/10.7298/fnca-gc79
dc.identifier.otherPandurangi_cornellgrad_0058F_12202
dc.identifier.otherhttp://dissertations.umi.com/cornellgrad:12202
dc.identifier.urihttps://hdl.handle.net/1813/103011
dc.language.isoen
dc.subjectBifurcation
dc.subjectLocalization
dc.subjectNonlinear Elasticity
dc.subjectStability
dc.titleSPATIAL LOCALIZATION IN NONLINEAR ELASTICITY VIA GLOBAL BIFURCATION
dc.typedissertation or thesis
dcterms.licensehttps://hdl.handle.net/1813/59810
thesis.degree.disciplineTheoretical and Applied Mechanics
thesis.degree.grantorCornell University
thesis.degree.levelDoctor of Philosophy
thesis.degree.namePh. D., Theoretical and Applied Mechanics

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Pandurangi_cornellgrad_0058F_12202.pdf
Size:
7.2 MB
Format:
Adobe Portable Document Format
Download

Collections

Cornell Theses and Dissertations