Statistical theory of dislocations in two-dimensional elastic bodies
We derive in this paper equations of continuously distributed dislocations in linear elastic media, starting from a finite number of dislocation lines perpendicular to the plane of the solid. Thus, dislocations are points with a structure and the non-material (but possessing field mass) dislocation...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
2000-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2000/239-256.pdf |
| _version_ | 1811240484109025280 |
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| author | H. Zorski |
| author_facet | H. Zorski |
| author_sort | H. Zorski |
| collection | DOAJ |
| description | We derive in this paper equations of continuously distributed dislocations in linear elastic media, starting from a finite number of dislocation lines perpendicular to the plane of the solid. Thus, dislocations are points with a structure and the non-material (but possessing field mass) dislocation “gas” is constructed by statistical means, following known procedures of the kinetic theory. A constitutive law for the kinetic stress tensor is postulated - the only one required in this theory. The result is a mixture of two interacting continua, governed by a system of 6 partial differential equations, for 3 displacements, 2 dislocation gas velocities and the dislocation density. Energy balance law is derived from the system of equations and some general properties of the latter are examined. One particular case is examined in more detail, namely screw dislocations. |
| first_indexed | 2024-04-12T13:20:04Z |
| format | Article |
| id | doaj.art-c7294fc7e64c43b7a7e1756dd6e2c0e1 |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-04-12T13:20:04Z |
| publishDate | 2000-01-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-c7294fc7e64c43b7a7e1756dd6e2c0e12022-12-22T03:31:31ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33502000-01-01201239256Statistical theory of dislocations in two-dimensional elastic bodiesH. Zorski0Polish Academy of SciencesWe derive in this paper equations of continuously distributed dislocations in linear elastic media, starting from a finite number of dislocation lines perpendicular to the plane of the solid. Thus, dislocations are points with a structure and the non-material (but possessing field mass) dislocation “gas” is constructed by statistical means, following known procedures of the kinetic theory. A constitutive law for the kinetic stress tensor is postulated - the only one required in this theory. The result is a mixture of two interacting continua, governed by a system of 6 partial differential equations, for 3 displacements, 2 dislocation gas velocities and the dislocation density. Energy balance law is derived from the system of equations and some general properties of the latter are examined. One particular case is examined in more detail, namely screw dislocations.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2000/239-256.pdfelastic bodydislocation fieldwaves in mixture |
| spellingShingle | H. Zorski Statistical theory of dislocations in two-dimensional elastic bodies Rendiconti di Matematica e delle Sue Applicazioni elastic body dislocation field waves in mixture |
| title | Statistical theory of dislocations in two-dimensional elastic bodies |
| title_full | Statistical theory of dislocations in two-dimensional elastic bodies |
| title_fullStr | Statistical theory of dislocations in two-dimensional elastic bodies |
| title_full_unstemmed | Statistical theory of dislocations in two-dimensional elastic bodies |
| title_short | Statistical theory of dislocations in two-dimensional elastic bodies |
| title_sort | statistical theory of dislocations in two dimensional elastic bodies |
| topic | elastic body dislocation field waves in mixture |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2000/239-256.pdf |
| work_keys_str_mv | AT hzorski statisticaltheoryofdislocationsintwodimensionalelasticbodies |