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Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework
Includes bibliographical references (p. [221]-239).
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Civil Engineering
2015
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| _version_ | 1867613148811362304 |
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| access_status_str | Open Access |
| author | McBride, Andrew Trevor |
| author2 | Reddy, B Daya |
| author_browse | McBride, Andrew Trevor Reddy, B Daya |
| author_facet | Reddy, B Daya McBride, Andrew Trevor |
| author_sort | McBride, Andrew Trevor |
| collection | Thesis |
| description | Includes bibliographical references (p. [221]-239). |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/10924 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:31.816Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Department of Civil Engineering |
| publisherStr | Department of Civil Engineering |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/10924 Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework McBride, Andrew Trevor Reddy, B Daya Includes bibliographical references (p. [221]-239). An investigation of a model of gradient plasticity in which the classical von Mises yield function is augmented by a term involving the Laplacian of the equivalent plastic strain is presented. The theory is developed within the framework of non-smooth convex analysis by exploiting the equivalence between the primal and dual expressions of the plastic deformation evolution relations. The nonlocal plastic evolution relations for the case of gradient plasticity are approximated using a discontinuous Galerkin finite element formulation. Both the small- and finite-strain theories are investigated. Considerable attention is focused on developing a firm mathematical foundation for the model of gradient plasticity restricted to the infinitesimal-strain regime. The key contributions arising from the analysis of the classical plasticity problem and the model of gradient plasticity include demonstrating the consistency of the variational formulation, and analyses of both the continuous-in-time and fully-discrete approximations; the error estimates obtained correspond to those for the conventional Galerkin approximations of the classical problem. The focus of the analysis is on those properties of the problem that would ensure existence of a unique solution for both hardening and softening problems. It is well known that classical finite element method simulations of softening problems are pathologically dependent on the discretisation. 2015-01-02T08:53:23Z 2015-01-02T08:53:23Z 2008 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/10924 eng application/pdf Department of Civil Engineering Faculty of Engineering and the Built Environment University of Cape Town |
| spellingShingle | McBride, Andrew Trevor Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework |
| thesis_degree_str | Doctoral |
| title | Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework |
| title_full | Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework |
| title_fullStr | Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework |
| title_full_unstemmed | Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework |
| title_short | Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework |
| title_sort | formulation analysis and solution algorithms for a model of gradient plasticity within a discontinuous galerkin framework |
| url | http://hdl.handle.net/11427/10924 |
| work_keys_str_mv | AT mcbrideandrewtrevor formulationanalysisandsolutionalgorithmsforamodelofgradientplasticitywithinadiscontinuousgalerkinframework |