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Numerical investigation of theories of strain-gradient plasticity
In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. This theory is based on that originally developed by Gurtin and Anand, and includes both dissipative and energetic contributions. A detailed numerical study is based on the problem of s...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2019
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| _version_ | 1867613190916931584 |
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| access_status_str | Open Access |
| author | Mhlongo, Nothando Precious |
| author2 | Reddy, Batmanathan D. |
| author_browse | Mhlongo, Nothando Precious Reddy, Batmanathan D. |
| author_facet | Reddy, Batmanathan D. Mhlongo, Nothando Precious |
| author_sort | Mhlongo, Nothando Precious |
| collection | Thesis |
| description | In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. This theory is based on that originally developed by Gurtin and Anand, and includes both dissipative and energetic contributions. A detailed numerical study is based on the problem of simple shear of a homogeneous and a non-homogeneous block. Combinations of micro-hard and micro-free boundary conditions are used. The elastic gap, that is, elastic behaviour following a change in the plastic regime from micro-free to micro-hard boundary conditions, is clearly evident. A second phenomenon studied is that of strengthening and hardening with increase in dissipative and energetic length scales, respectively. For the purely dissipative theory, it has been shown that the flow relation in terms of Cauchy stress is necessarily global in terms of the dissipation function. This relation cannot be inverted in closed form to obtain a relation in terms of a global yield function. Approximations to the yield function are proposed using a maximisation relation, and these predictions of yield are compared with actual yield determined numerically. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/30048 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:13.078Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2019 |
| publishDateRange | 2019 |
| publishDateSort | 2019 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/30048 Numerical investigation of theories of strain-gradient plasticity Mhlongo, Nothando Precious Reddy, Batmanathan D. In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. This theory is based on that originally developed by Gurtin and Anand, and includes both dissipative and energetic contributions. A detailed numerical study is based on the problem of simple shear of a homogeneous and a non-homogeneous block. Combinations of micro-hard and micro-free boundary conditions are used. The elastic gap, that is, elastic behaviour following a change in the plastic regime from micro-free to micro-hard boundary conditions, is clearly evident. A second phenomenon studied is that of strengthening and hardening with increase in dissipative and energetic length scales, respectively. For the purely dissipative theory, it has been shown that the flow relation in terms of Cauchy stress is necessarily global in terms of the dissipation function. This relation cannot be inverted in closed form to obtain a relation in terms of a global yield function. Approximations to the yield function are proposed using a maximisation relation, and these predictions of yield are compared with actual yield determined numerically. 2019-05-10T12:04:45Z 2019-05-10T12:04:45Z 2018 2019-05-07T09:37:10Z Master Thesis Masters MSc http://hdl.handle.net/11427/30048 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Mhlongo, Nothando Precious Numerical investigation of theories of strain-gradient plasticity |
| thesis_degree_str | Master's |
| title | Numerical investigation of theories of strain-gradient plasticity |
| title_full | Numerical investigation of theories of strain-gradient plasticity |
| title_fullStr | Numerical investigation of theories of strain-gradient plasticity |
| title_full_unstemmed | Numerical investigation of theories of strain-gradient plasticity |
| title_short | Numerical investigation of theories of strain-gradient plasticity |
| title_sort | numerical investigation of theories of strain gradient plasticity |
| url | http://hdl.handle.net/11427/30048 |
| work_keys_str_mv | AT mhlongonothandoprecious numericalinvestigationoftheoriesofstraingradientplasticity |