On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media
For micropolar media we present a new definition of the local material symmetry group considering invariant properties of the both kinetic energy and strain energy density under changes of a reference placement. Unlike simple (Cauchy) materials, micropolar media can be characterized through two kine...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/10/1632 |
| _version_ | 1797551810511110144 |
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| author | Victor A. Eremeyev Violetta Konopińska-Zmysłowska |
| author_facet | Victor A. Eremeyev Violetta Konopińska-Zmysłowska |
| author_sort | Victor A. Eremeyev |
| collection | DOAJ |
| description | For micropolar media we present a new definition of the local material symmetry group considering invariant properties of the both kinetic energy and strain energy density under changes of a reference placement. Unlike simple (Cauchy) materials, micropolar media can be characterized through two kinematically independent fields, that are translation vector and orthogonal microrotation tensor. In other words, in micropolar continua we have six degrees of freedom (DOF) that are three DOFs for translations and three DOFs for rotations. So the corresponding kinetic energy density nontrivially depends on linear and angular velocity. Here we define the local material symmetry group as a set of ordered triples of tensors which keep both kinetic energy density and strain energy density unchanged during the related change of a reference placement. The triples were obtained using transformation rules of strain measures and microinertia tensors under replacement of a reference placement. From the physical point of view, the local material symmetry group consists of such density-preserving transformations of a reference placement, that cannot be experimentally detected. So the constitutive relations become invariant under such transformations. Knowing a priori a material’s symmetry, one can establish a simplified form of constitutive relations. In particular, the number of independent arguments in constitutive relations could be significantly reduced. |
| first_indexed | 2024-03-10T15:51:22Z |
| format | Article |
| id | doaj.art-00956937fc2b4dd28e9cae0122e1dc56 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T15:51:22Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-00956937fc2b4dd28e9cae0122e1dc562023-11-20T15:59:18ZengMDPI AGSymmetry2073-89942020-10-011210163210.3390/sym12101632On Dynamic Extension of a Local Material Symmetry Group for Micropolar MediaVictor A. Eremeyev0Violetta Konopińska-Zmysłowska1Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, 80-233 Gdansk, PolandFaculty of Civil and Environmental Engineering, Gdańsk University of Technology, 80-233 Gdansk, PolandFor micropolar media we present a new definition of the local material symmetry group considering invariant properties of the both kinetic energy and strain energy density under changes of a reference placement. Unlike simple (Cauchy) materials, micropolar media can be characterized through two kinematically independent fields, that are translation vector and orthogonal microrotation tensor. In other words, in micropolar continua we have six degrees of freedom (DOF) that are three DOFs for translations and three DOFs for rotations. So the corresponding kinetic energy density nontrivially depends on linear and angular velocity. Here we define the local material symmetry group as a set of ordered triples of tensors which keep both kinetic energy density and strain energy density unchanged during the related change of a reference placement. The triples were obtained using transformation rules of strain measures and microinertia tensors under replacement of a reference placement. From the physical point of view, the local material symmetry group consists of such density-preserving transformations of a reference placement, that cannot be experimentally detected. So the constitutive relations become invariant under such transformations. Knowing a priori a material’s symmetry, one can establish a simplified form of constitutive relations. In particular, the number of independent arguments in constitutive relations could be significantly reduced.https://www.mdpi.com/2073-8994/12/10/1632micropolar continuumlocal symmetry groupkinetic constitutive equationCosserat continuumanisotropy |
| spellingShingle | Victor A. Eremeyev Violetta Konopińska-Zmysłowska On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media Symmetry micropolar continuum local symmetry group kinetic constitutive equation Cosserat continuum anisotropy |
| title | On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media |
| title_full | On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media |
| title_fullStr | On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media |
| title_full_unstemmed | On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media |
| title_short | On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media |
| title_sort | on dynamic extension of a local material symmetry group for micropolar media |
| topic | micropolar continuum local symmetry group kinetic constitutive equation Cosserat continuum anisotropy |
| url | https://www.mdpi.com/2073-8994/12/10/1632 |
| work_keys_str_mv | AT victoraeremeyev ondynamicextensionofalocalmaterialsymmetrygroupformicropolarmedia AT violettakonopinskazmysłowska ondynamicextensionofalocalmaterialsymmetrygroupformicropolarmedia |