A note on frame indifference and material isomorphism for simple materials
(2015) In Mathematics and Mechanics of Solids 20(4). p.461-479- Abstract
- In conventional presentations of continuum mechanics, the reference placement of a solid body is taken to be independent of the observer. Furthermore, the Euclidean spaces associated with different frames of reference are taken to be identical. In this paper these assumption are abandoned and different framings, as well as reference placements, will correspond to different Euclidean spaces. This requires a modified formulation of the principle of frame indifference for constitutive response functions. Consequences of this approach are investigated in terms of transformation formulas for kinematical and dynamical quantities and the reduction of constitutive equations for simple materials. A relation between material symmetry groups,... (More)
- In conventional presentations of continuum mechanics, the reference placement of a solid body is taken to be independent of the observer. Furthermore, the Euclidean spaces associated with different frames of reference are taken to be identical. In this paper these assumption are abandoned and different framings, as well as reference placements, will correspond to different Euclidean spaces. This requires a modified formulation of the principle of frame indifference for constitutive response functions. Consequences of this approach are investigated in terms of transformation formulas for kinematical and dynamical quantities and the reduction of constitutive equations for simple materials. A relation between material symmetry groups, relative to different framings, is derived. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5401651
- author
- Lidström, Per LU
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Continuum mechanics, framings, objectivity, frame indifference, material, isomorphism
- in
- Mathematics and Mechanics of Solids
- volume
- 20
- issue
- 4
- pages
- 461 - 479
- publisher
- SAGE Publications
- external identifiers
-
- wos:000352536700004
- scopus:84926507979
- ISSN
- 1741-3028
- DOI
- 10.1177/1081286513503069
- language
- English
- LU publication?
- yes
- id
- 904d7cf7-f2b0-41ce-8624-587299bc3ea2 (old id 5401651)
- date added to LUP
- 2016-04-01 10:38:17
- date last changed
- 2022-04-12 08:08:49
@article{904d7cf7-f2b0-41ce-8624-587299bc3ea2,
abstract = {{In conventional presentations of continuum mechanics, the reference placement of a solid body is taken to be independent of the observer. Furthermore, the Euclidean spaces associated with different frames of reference are taken to be identical. In this paper these assumption are abandoned and different framings, as well as reference placements, will correspond to different Euclidean spaces. This requires a modified formulation of the principle of frame indifference for constitutive response functions. Consequences of this approach are investigated in terms of transformation formulas for kinematical and dynamical quantities and the reduction of constitutive equations for simple materials. A relation between material symmetry groups, relative to different framings, is derived.}},
author = {{Lidström, Per}},
issn = {{1741-3028}},
keywords = {{Continuum mechanics; framings; objectivity; frame indifference; material; isomorphism}},
language = {{eng}},
number = {{4}},
pages = {{461--479}},
publisher = {{SAGE Publications}},
series = {{Mathematics and Mechanics of Solids}},
title = {{A note on frame indifference and material isomorphism for simple materials}},
url = {{http://dx.doi.org/10.1177/1081286513503069}},
doi = {{10.1177/1081286513503069}},
volume = {{20}},
year = {{2015}},
}