Reformulation of continuum defects in terms of the general teleparallel geometry in the language of exterior algebra
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917978421854208 |
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| author | Adak, Muzaffer Dereli, Tekin Kok, Ertan Sert, Ozcan |
| author_facet | Adak, Muzaffer Dereli, Tekin Kok, Ertan Sert, Ozcan |
| contents | We discuss the geometric formulation of continuum defects consisting of dislocations and disclinations. After reviewing the metric affine geometry and the present geometric formulation of dislocation and disclination written in terms of torsion and full curvature (together with vanishing non-metricity), we give a new formulation of them in a novel way in terms of torsion and non-metricity (together with vanishing full curvature), the so-called general teleparallel geometry. All calculations are performed by using the exterior algebra. We obtain continuity equations explicitly for dislocation density and disclination density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06184 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reformulation of continuum defects in terms of the general teleparallel geometry in the language of exterior algebra Adak, Muzaffer Dereli, Tekin Kok, Ertan Sert, Ozcan Mathematical Physics Materials Science We discuss the geometric formulation of continuum defects consisting of dislocations and disclinations. After reviewing the metric affine geometry and the present geometric formulation of dislocation and disclination written in terms of torsion and full curvature (together with vanishing non-metricity), we give a new formulation of them in a novel way in terms of torsion and non-metricity (together with vanishing full curvature), the so-called general teleparallel geometry. All calculations are performed by using the exterior algebra. We obtain continuity equations explicitly for dislocation density and disclination density. |
| title | Reformulation of continuum defects in terms of the general teleparallel geometry in the language of exterior algebra |
| topic | Mathematical Physics Materials Science |
| url | https://arxiv.org/abs/2408.06184 |