Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework

 

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dc.contributor.advisor Reddy, B Daya en_ZA
dc.contributor.author McBride, Andrew Trevor en_ZA
dc.date.accessioned 2015-01-02T08:53:23Z
dc.date.available 2015-01-02T08:53:23Z
dc.date.issued 2008 en_ZA
dc.identifier.citation McBride, A. 2008. Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/10924
dc.description Includes bibliographical references (p. [221]-239). en_ZA
dc.description.abstract 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. en_ZA
dc.language.iso eng en_ZA
dc.title Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework en_ZA
dc.type Doctoral Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Engineering and the Built Environment
dc.publisher.department Department of Civil Engineering en_ZA
dc.type.qualificationlevel Doctoral
dc.type.qualificationname PhD en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation McBride, A. T. (2008). <i>Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework</i>. (Thesis). University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering. Retrieved from http://hdl.handle.net/11427/10924 en_ZA
dc.identifier.chicagocitation McBride, Andrew Trevor. <i>"Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework."</i> Thesis., University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering, 2008. http://hdl.handle.net/11427/10924 en_ZA
dc.identifier.vancouvercitation McBride AT. Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework. [Thesis]. University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering, 2008 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/10924 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - McBride, Andrew Trevor AB - 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. DA - 2008 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2008 T1 - Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework TI - Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework UR - http://hdl.handle.net/11427/10924 ER - en_ZA


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