Geometrical modeling and numerical analysis of screw dislocation
This study conducts the modeling and numerical analysis of a screw dislocation in a three-dimensional continuous medium. Our modeling is based on the differential geometry of Weitzenböck manifold, i.e., a Riemann-Cartan manifold which equips itself with non-zero torsion in the affine connection. Fol...
| Main Authors: | , |
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| Format: | Article |
| Language: | Japanese |
| Published: |
The Japan Society of Mechanical Engineers
2021-01-01
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| Series: | Nihon Kikai Gakkai ronbunshu |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/transjsme/87/894/87_20-00409/_pdf/-char/en |
| _version_ | 1811308699147304960 |
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| author | Shunsuke KOBAYASHI Ryuichi TARUMI |
| author_facet | Shunsuke KOBAYASHI Ryuichi TARUMI |
| author_sort | Shunsuke KOBAYASHI |
| collection | DOAJ |
| description | This study conducts the modeling and numerical analysis of a screw dislocation in a three-dimensional continuous medium. Our modeling is based on the differential geometry of Weitzenböck manifold, i.e., a Riemann-Cartan manifold which equips itself with non-zero torsion in the affine connection. Following to the standard framework of geometrical elasto-plasticity, we introduce the three smooth manifolds representing the reference R, intermediate B and current S configurations and express the kinematics using the diffeomorphisms between them. Our primary concern is the geometrical construction of the intermediate configuration B. For a given dislocation density τ, we calculated the plastic distorsion Fp through the integration of τ by homotopy operator. This analysis yields the dual frame ϑ of the Cartan moving frame, which satisfies the first structure equation and Bianchi identity, simultaneously. The current configuration S is obtained by embedding of B to the conventional Euclidean space R3 so as to minimize the strain energy functional. The variational problem is solved numerically using the isogeometric analysis; Galerkin method with non-uniform rational B-spline basis functions. Present analysis revealed that far-field stresses around a screw dislocation agree quantitatively well with those of the Volterra dislocation. A notable difference is non-singularity at the dislocation core. Another remarkable feature is the emergence of hydrostatic pressure due to the geometrical nonlinearity. We also found that surface displacements include a vortex centered at the dislocation line. This is a realization of Eshelby twist. |
| first_indexed | 2024-04-13T09:27:54Z |
| format | Article |
| id | doaj.art-8f62c191bf7f481c8d738110ea707f5f |
| institution | Directory Open Access Journal |
| issn | 2187-9761 |
| language | Japanese |
| last_indexed | 2024-04-13T09:27:54Z |
| publishDate | 2021-01-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Nihon Kikai Gakkai ronbunshu |
| spelling | doaj.art-8f62c191bf7f481c8d738110ea707f5f2022-12-22T02:52:22ZjpnThe Japan Society of Mechanical EngineersNihon Kikai Gakkai ronbunshu2187-97612021-01-018789420-0040920-0040910.1299/transjsme.20-00409transjsmeGeometrical modeling and numerical analysis of screw dislocationShunsuke KOBAYASHI0Ryuichi TARUMI1Graduate School of Engineering Science, Osaka UniversityGraduate School of Engineering Science, Osaka UniversityThis study conducts the modeling and numerical analysis of a screw dislocation in a three-dimensional continuous medium. Our modeling is based on the differential geometry of Weitzenböck manifold, i.e., a Riemann-Cartan manifold which equips itself with non-zero torsion in the affine connection. Following to the standard framework of geometrical elasto-plasticity, we introduce the three smooth manifolds representing the reference R, intermediate B and current S configurations and express the kinematics using the diffeomorphisms between them. Our primary concern is the geometrical construction of the intermediate configuration B. For a given dislocation density τ, we calculated the plastic distorsion Fp through the integration of τ by homotopy operator. This analysis yields the dual frame ϑ of the Cartan moving frame, which satisfies the first structure equation and Bianchi identity, simultaneously. The current configuration S is obtained by embedding of B to the conventional Euclidean space R3 so as to minimize the strain energy functional. The variational problem is solved numerically using the isogeometric analysis; Galerkin method with non-uniform rational B-spline basis functions. Present analysis revealed that far-field stresses around a screw dislocation agree quantitatively well with those of the Volterra dislocation. A notable difference is non-singularity at the dislocation core. Another remarkable feature is the emergence of hydrostatic pressure due to the geometrical nonlinearity. We also found that surface displacements include a vortex centered at the dislocation line. This is a realization of Eshelby twist.https://www.jstage.jst.go.jp/article/transjsme/87/894/87_20-00409/_pdf/-char/enscrew dislocationdifferential geometryweitzenböck manifoldelasto-plasticitystress field |
| spellingShingle | Shunsuke KOBAYASHI Ryuichi TARUMI Geometrical modeling and numerical analysis of screw dislocation Nihon Kikai Gakkai ronbunshu screw dislocation differential geometry weitzenböck manifold elasto-plasticity stress field |
| title | Geometrical modeling and numerical analysis of screw dislocation |
| title_full | Geometrical modeling and numerical analysis of screw dislocation |
| title_fullStr | Geometrical modeling and numerical analysis of screw dislocation |
| title_full_unstemmed | Geometrical modeling and numerical analysis of screw dislocation |
| title_short | Geometrical modeling and numerical analysis of screw dislocation |
| title_sort | geometrical modeling and numerical analysis of screw dislocation |
| topic | screw dislocation differential geometry weitzenböck manifold elasto-plasticity stress field |
| url | https://www.jstage.jst.go.jp/article/transjsme/87/894/87_20-00409/_pdf/-char/en |
| work_keys_str_mv | AT shunsukekobayashi geometricalmodelingandnumericalanalysisofscrewdislocation AT ryuichitarumi geometricalmodelingandnumericalanalysisofscrewdislocation |