On Volume Average Relations in Continuum Mechanics, Part I
(2006) In Research report- 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/789668
- author
- Lidström, Per LU
- organization
- publishing date
- 2006
- type
- Book/Report
- publication status
- published
- subject
- keywords
- volume average relations, Continuum mechanics, homogenization.
- in
- Research report
- pages
- 55 pages
- publisher
- Department of Mechanical Engineering, Lund University
- report number
- ISRN LUTFD2/TFME-06/1001-SE
- language
- English
- LU publication?
- yes
- id
- 05e3f419-77ec-4c30-bbb5-fca7ac9e52a5 (old id 789668)
- date added to LUP
- 2016-04-04 12:25:03
- date last changed
- 2018-11-21 21:10:50
@techreport{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}},
institution = {{Department of Mechanical Engineering, Lund University}},
keywords = {{volume average relations; Continuum mechanics; homogenization.}},
language = {{eng}},
number = {{ISRN LUTFD2/TFME-06/1001-SE}},
series = {{Research report}},
title = {{On Volume Average Relations in Continuum Mechanics, Part I}},
year = {{2006}},
}