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On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media

Abstrakt

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.

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Informacje szczegółowe

Kategoria:
Publikacja w czasopiśmie
Typ:
artykuły w czasopismach
Opublikowano w:
Symmetry-Basel nr 10,
ISSN: 2073-8994
Język:
angielski
Rok wydania:
2020
Opis bibliograficzny:
Eremeev V., Konopińska-Zmysłowska V.: On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media// Symmetry-Basel -Vol. 10,iss. 12 (2020), s.1632-
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.3390/sym12101632
Weryfikacja:
Politechnika Gdańska

wyświetlono 5 razy

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