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Analysis of the volume averaging relations in continuum mechanics

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Author

Summary, in English

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.

Department/s

Publishing year

2012

Language

English

Pages

476-505

Publication/Series

Mathematics and Mechanics of Solids

Volume

18

Issue

5

Document type

Journal article

Publisher

SAGE Publications

Topic

  • Applied Mechanics

Keywords

  • volume average relations
  • computational homogenization
  • continuum mechanics
  • periodic boundary conditions
  • representative volume element

Status

Published

ISBN/ISSN/Other

  • ISSN: 1741-3028