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A note on frame indifference and material isomorphism for simple materials

Lidström, Per LU (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)
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author
organization
publishing date
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 Inc.
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
2015-05-19 12:34:10
date last changed
2017-01-01 03:45:59
@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},
  keyword      = {Continuum mechanics,framings,objectivity,frame indifference,material,isomorphism},
  language     = {eng},
  number       = {4},
  pages        = {461--479},
  publisher    = {SAGE Publications Inc.},
  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},
  volume       = {20},
  year         = {2015},
}