Granular Flow Models: Analysis and Numerical Simulations
| dc.contributor.advisor | Hien T. Tran, Committee Member | en_US |
| dc.contributor.advisor | Stephen Schecter, Committee Member | en_US |
| dc.contributor.advisor | Michael Shearer, Committee Chair | en_US |
| dc.contributor.advisor | Pierre A. Gremaud, Committee Member | en_US |
| dc.contributor.author | Wieman, Robert E. | en_US |
| dc.date.accessioned | 2010-04-02T19:21:30Z | |
| dc.date.available | 2010-04-02T19:21:30Z | |
| dc.date.issued | 2003-09-15 | en_US |
| dc.degree.discipline | Applied Mathematics | en_US |
| dc.degree.level | dissertation | en_US |
| dc.degree.name | PhD | en_US |
| dc.description | North Carolina State University Theses Mathematics. | |
| dc.description.abstract | We study elastoplastic transitions in solutions of the antiplane shear model of granular flow, and describe a time-periodic solution that arises when the antiplane shear model is discretized in space. The antiplane shear model is a simplification of the continuum equations representing the flow of granular materials. The modeling of granular flow has many applications, from agricultural silos to geomechanics: improved accuracy in modeling will lead to safer and more economical designs for silos and industrial hoppers, and make oil drilling a more efficient process. We construct approximate solutions to the antiplane shear model with piecewise linear initial data, which feature transitions between elastic and plastic states. These transitions travel with fixed speed. Numerical simulations demonstrate that the same elastoplastic transitions are the prominent features of the numerical solution. The periodic solution of discretized antiplane shear appears at a critical value of the elasticity parameter for antiplane shear. The bifurcation to a periodic solution appears to be a Hopf bifurcation. The periodic solution contains elastoplastic transitions, as well as a shear band that appears over part of the period. Away from the shear band, the periodic solution has four distinct regions, three elastic and one plastic. Refinement of the spatial discretization further resolves these states. | en_US |
| dc.format | Thesis (Ph.D.)--North Carolina State University. | |
| dc.identifier.other | etd-08142003-161200 | en_US |
| dc.identifier.uri | http://www.lib.ncsu.edu/resolver/1840.16/5872 | |
| dc.rights | I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. | en_US |
| dc.subject | antiplane shear model | en_US |
| dc.subject | granular materials | en_US |
| dc.title | Granular Flow Models: Analysis and Numerical Simulations | en_US |
| dcterms.abstract | Keywords: antiplane shear model, granular materials. | |
| dcterms.extent | ix, 87 pages : illustrations (some color) |
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