RT Journal Article
ID 44f01b9c3c201550
A1 Ben Bettaieb, Mohamed
A1 Debordes, Olivier
A1 Dogui, Abdelwaheb
A1 Duchene, Laurent
T1 AVERAGING PROPERTIES FOR PERIODIC HOMOGENIZATION AND LARGE DEFORMATION
JF International Journal for Multiscale Computational Engineering
JO JMC
YR 2012
FD 2012-03-30
VO 10
IS 3
SP 281
OP 293
K1 periodic homogenization
K1 large deformation
K1 Lagrangian formulation
K1 Eulerianformulation
AB The main motivation of this paper consists of using the periodic homogenization theory to derive several relations between macroscopic Lagrangian (e.g., deformation gradient, Piola−Kirchhoff tensor) and Eulerian (e.g., velocity gradient, Cauchy stress) quantities. These relations demonstrate that these macroscopic quantities behave formally in the same way as their microscopic counterparts. We say therefore that these relations are stable with respect to the periodic homogenization. We also demonstrate the equivalence between the two forms of the macroscopic power density expressed in the Lagrangian and Eulerian formulations. Two simple examples illustrate these results, and indicate also that the Green−Lagrange strain tensor and the second Piola−Kirchhoff stress tensor are not stable with respect to periodic homogenization.
PB Begell House
LK http://dl.begellhouse.com/journals/61fd1b191cf7e96f,20e1ba4b4b9313c6,44f01b9c3c201550.html