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On Volume Average Relations in Continuum Mechanics, Part I

Lidström, Per LU (2006) In Research report ISRN LUTFD2/TFME-06/1001-SE.
Abstract
In this paper, and in the one to follow, an analysis of volume average relations in classical continuum mechanics is presented. Results from various investigations, previously presented in the literature, have been reviewed and extended and they have, in some cases, been more precisely stated and rigorously proven. Some of the results presented are believed to be new. The key object for the paper is the investigation of the concept of volume average consistence for continuum mechanical relations and the derivation of various integral formulas for volume averaged quantities. This paper is restricted to basic kinematics, mass, momentum and moment of momentum. The implications of the so-called Hill’s condition have been elucidated. A... (More)
In this paper, and in the one to follow, an analysis of volume average relations in classical continuum mechanics is presented. Results from various investigations, previously presented in the literature, have been reviewed and extended and they have, in some cases, been more precisely stated and rigorously proven. Some of the results presented are believed to be new. The key object for the paper is the investigation of the concept of volume average consistence for continuum mechanical relations and the derivation of various integral formulas for volume averaged quantities. This paper is restricted to basic kinematics, mass, momentum and moment of momentum. The implications of the so-called Hill’s condition have been elucidated. A discussion of volume average relations concerning energy, net power and entropy will be postponed to a forthcoming paper. Applications to micromechanics will sometimes require the possibility of introducing different types of singularities into the thermo-mechanical description, such as singular surfaces and cracks. Here it is assumed that cracks are absent but singular surfaces giving rise to jump discontinuities in the thermo-mechanical variables are allowed for. (Less)
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author
organization
publishing date
type
Book/Report
publication status
published
subject
keywords
volume average relations, Continuum mechanics, homogenization.
in
Research report
volume
ISRN LUTFD2/TFME-06/1001-SE
pages
55 pages
publisher
Department of Mechanical Engineering, Lund University
language
English
LU publication?
yes
id
05e3f419-77ec-4c30-bbb5-fca7ac9e52a5 (old id 789668)
date added to LUP
2008-02-08 10:50:18
date last changed
2016-04-16 10:32:33
@misc{05e3f419-77ec-4c30-bbb5-fca7ac9e52a5,
  abstract     = {In this paper, and in the one to follow, an analysis of volume average relations in classical continuum mechanics is presented. Results from various investigations, previously presented in the literature, have been reviewed and extended and they have, in some cases, been more precisely stated and rigorously proven. Some of the results presented are believed to be new. The key object for the paper is the investigation of the concept of volume average consistence for continuum mechanical relations and the derivation of various integral formulas for volume averaged quantities. This paper is restricted to basic kinematics, mass, momentum and moment of momentum. The implications of the so-called Hill’s condition have been elucidated. A discussion of volume average relations concerning energy, net power and entropy will be postponed to a forthcoming paper. Applications to micromechanics will sometimes require the possibility of introducing different types of singularities into the thermo-mechanical description, such as singular surfaces and cracks. Here it is assumed that cracks are absent but singular surfaces giving rise to jump discontinuities in the thermo-mechanical variables are allowed for.},
  author       = {Lidström, Per},
  keyword      = {volume average relations,Continuum mechanics,homogenization.},
  language     = {eng},
  pages        = {55},
  publisher    = {ARRAY(0x7f2cee0)},
  series       = {Research report},
  title        = {On Volume Average Relations in Continuum Mechanics, Part I},
  volume       = {ISRN LUTFD2/TFME-06/1001-SE},
  year         = {2006},
}