Differential Geometry Approach to Continuous Model of Micro-Structural Defects in Finite Elasto-Plasticity
This paper concerns finite elasto-plasticity of crystalline materials with micro-structural defects. We revisit the basic concepts: plastic distortion and decomposition of the plastic connection. The body is endowed with a structure of differential manifold. The plastic distortion is an incompatible...
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| Format: | Article |
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MDPI AG
2021-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/12/2340 |
| _version_ | 1797500326609158144 |
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| author | Sanda Cleja-Ţigoiu |
| author_facet | Sanda Cleja-Ţigoiu |
| author_sort | Sanda Cleja-Ţigoiu |
| collection | DOAJ |
| description | This paper concerns finite elasto-plasticity of crystalline materials with micro-structural defects. We revisit the basic concepts: plastic distortion and decomposition of the plastic connection. The body is endowed with a structure of differential manifold. The plastic distortion is an incompatible diffeomorphism. The metric induced by the plastic distortion on the intermediate configuration (considered to be a differential manifold) is a key point in the theory, in defining the defects related to point defects, or extra-matter. The so-called plastic connection is metric, with plastic metric tensor expressed in terms of the plastic distortion and its adjoint. We prove an appropriate decomposition of the plastic connection, without any supposition concerning the non-metricity of plastic connection. All types of the lattice defects, dislocations, disclinations, and point defects are described in terms of the densities related to the elements that characterize the decomposition theorem for plastic connection. As a novelty, the measure of the interplay of the possible lattice defects is introduced via the Cartan torsion tensor. To justify the given definitions, the proposed measures of defects are compared to their counterparts corresponding to a classical framework of continuum mechanics. Thus, their physical meanings can be emphasized at once. |
| first_indexed | 2024-03-10T03:00:18Z |
| format | Article |
| id | doaj.art-b8d769be238344a99ebdf99cd3e16ed5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T03:00:18Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b8d769be238344a99ebdf99cd3e16ed52023-11-23T10:45:44ZengMDPI AGSymmetry2073-89942021-12-011312234010.3390/sym13122340Differential Geometry Approach to Continuous Model of Micro-Structural Defects in Finite Elasto-PlasticitySanda Cleja-Ţigoiu0Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, RomaniaThis paper concerns finite elasto-plasticity of crystalline materials with micro-structural defects. We revisit the basic concepts: plastic distortion and decomposition of the plastic connection. The body is endowed with a structure of differential manifold. The plastic distortion is an incompatible diffeomorphism. The metric induced by the plastic distortion on the intermediate configuration (considered to be a differential manifold) is a key point in the theory, in defining the defects related to point defects, or extra-matter. The so-called plastic connection is metric, with plastic metric tensor expressed in terms of the plastic distortion and its adjoint. We prove an appropriate decomposition of the plastic connection, without any supposition concerning the non-metricity of plastic connection. All types of the lattice defects, dislocations, disclinations, and point defects are described in terms of the densities related to the elements that characterize the decomposition theorem for plastic connection. As a novelty, the measure of the interplay of the possible lattice defects is introduced via the Cartan torsion tensor. To justify the given definitions, the proposed measures of defects are compared to their counterparts corresponding to a classical framework of continuum mechanics. Thus, their physical meanings can be emphasized at once.https://www.mdpi.com/2073-8994/13/12/2340elasto-plasticitylattice defectsplastic distortionplastic connectiondifferential manifolds |
| spellingShingle | Sanda Cleja-Ţigoiu Differential Geometry Approach to Continuous Model of Micro-Structural Defects in Finite Elasto-Plasticity Symmetry elasto-plasticity lattice defects plastic distortion plastic connection differential manifolds |
| title | Differential Geometry Approach to Continuous Model of Micro-Structural Defects in Finite Elasto-Plasticity |
| title_full | Differential Geometry Approach to Continuous Model of Micro-Structural Defects in Finite Elasto-Plasticity |
| title_fullStr | Differential Geometry Approach to Continuous Model of Micro-Structural Defects in Finite Elasto-Plasticity |
| title_full_unstemmed | Differential Geometry Approach to Continuous Model of Micro-Structural Defects in Finite Elasto-Plasticity |
| title_short | Differential Geometry Approach to Continuous Model of Micro-Structural Defects in Finite Elasto-Plasticity |
| title_sort | differential geometry approach to continuous model of micro structural defects in finite elasto plasticity |
| topic | elasto-plasticity lattice defects plastic distortion plastic connection differential manifolds |
| url | https://www.mdpi.com/2073-8994/13/12/2340 |
| work_keys_str_mv | AT sandaclejatigoiu differentialgeometryapproachtocontinuousmodelofmicrostructuraldefectsinfiniteelastoplasticity |