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Analysis of the volume averaging relations in continuum mechanics

Ahadi, Aylin LU and Lidström, Per LU (2012) In Mathematics and Mechanics of Solids
Abstract
In this paper volume average relations related to the multilevel modeling process in continuum mechanics are analyzed and the concept of average consistency is investigated both analytically and numerically. These volume averages are used in the computational homogenization technique, where a transition of the mechanical properties from the local, microscopic, to the global, macroscopic, length scale is obtained. The Representative Volume Element (RVE) is used as a reference placement and the solution, in terms of volume averaged stress, will depend on which boundary conditions are chosen for the RVE. Three types of boundary conditions - periodic, affine and anti-periodic boundary condition are analyzed with respect to the average... (More)
In this paper volume average relations related to the multilevel modeling process in continuum mechanics are analyzed and the concept of average consistency is investigated both analytically and numerically. These volume averages are used in the computational homogenization technique, where a transition of the mechanical properties from the local, microscopic, to the global, macroscopic, length scale is obtained. The Representative Volume Element (RVE) is used as a reference placement and the solution, in terms of volume averaged stress, will depend on which boundary conditions are chosen for the RVE. Three types of boundary conditions - periodic, affine and anti-periodic boundary condition are analyzed with respect to the average consistence for the kinematical and stress relations used in continuum mechanics. The inconsistence is quantified by introducing the inconsistence ratio. It is shown analytically, that some average stress relations are fulfilled, assuming periodic boundary condition and anti-periodic traction vector, whereas the average relations connected to the deformation, are in general not average consistent. The inconsistence is investigated in a plane model using finite element technique. The numerical investigation has shown that the inconsistence ratios related to the deformation are also average consistent in the examples considered. (Less)
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Contribution to journal
publication status
in press
subject
keywords
volume average relations, computational homogenization, continuum mechanics, periodic boundary conditions, representative volume element
in
Mathematics and Mechanics of Solids
publisher
SAGE Publications Inc.
ISSN
1741-3028
language
English
LU publication?
yes
id
accd50a1-c274-4964-bf57-6ce96778b288 (old id 2296618)
date added to LUP
2012-01-19 13:06:57
date last changed
2016-04-15 15:39:08
@article{accd50a1-c274-4964-bf57-6ce96778b288,
  abstract     = {In this paper volume average relations related to the multilevel modeling process in continuum mechanics are analyzed and the concept of average consistency is investigated both analytically and numerically. These volume averages are used in the computational homogenization technique, where a transition of the mechanical properties from the local, microscopic, to the global, macroscopic, length scale is obtained. The Representative Volume Element (RVE) is used as a reference placement and the solution, in terms of volume averaged stress, will depend on which boundary conditions are chosen for the RVE. Three types of boundary conditions - periodic, affine and anti-periodic boundary condition are analyzed with respect to the average consistence for the kinematical and stress relations used in continuum mechanics. The inconsistence is quantified by introducing the inconsistence ratio. It is shown analytically, that some average stress relations are fulfilled, assuming periodic boundary condition and anti-periodic traction vector, whereas the average relations connected to the deformation, are in general not average consistent. The inconsistence is investigated in a plane model using finite element technique. The numerical investigation has shown that the inconsistence ratios related to the deformation are also average consistent in the examples considered.},
  author       = {Ahadi, Aylin and Lidström, Per},
  issn         = {1741-3028},
  keyword      = {volume average relations,computational homogenization,continuum mechanics,periodic boundary conditions,representative volume element},
  language     = {eng},
  publisher    = {SAGE Publications Inc.},
  series       = {Mathematics and Mechanics of Solids},
  title        = {Analysis of the volume averaging relations in continuum mechanics},
  year         = {2012},
}