Bounds are obtained on the volume fraction in a two-dimensional body containing two elastically isotropic materials with known bulk and shear moduli. These bounds use information about the average stress and strain fields, energy, determinant of the stress, and determinant of the displacement gradient, which can be determined from measurements of the traction and displacement at the boundary. The bounds are sharp if in each phase certain displacement gradient field components are constant. The inequalities we obtain also directly give bounds on the possible (average stress, average strain) pairs in a two-phase, two-dimensional, periodic or statistically homogeneous composite.
@article{CRMECA_2012__340_4-5_193_0,
author = {Graeme Walter Milton and Loc Hoang Nguyen},
title = {Bounds on the volume fraction of 2-phase, 2-dimensional elastic bodies and on (stress, strain) pairs in composites},
journal = {Comptes Rendus. M\'ecanique},
pages = {193--204},
publisher = {Elsevier},
volume = {340},
number = {4-5},
year = {2012},
doi = {10.1016/j.crme.2012.02.002},
language = {en},
}
TY - JOUR AU - Graeme Walter Milton AU - Loc Hoang Nguyen TI - Bounds on the volume fraction of 2-phase, 2-dimensional elastic bodies and on (stress, strain) pairs in composites JO - Comptes Rendus. Mécanique PY - 2012 SP - 193 EP - 204 VL - 340 IS - 4-5 PB - Elsevier DO - 10.1016/j.crme.2012.02.002 LA - en ID - CRMECA_2012__340_4-5_193_0 ER -
%0 Journal Article %A Graeme Walter Milton %A Loc Hoang Nguyen %T Bounds on the volume fraction of 2-phase, 2-dimensional elastic bodies and on (stress, strain) pairs in composites %J Comptes Rendus. Mécanique %D 2012 %P 193-204 %V 340 %N 4-5 %I Elsevier %R 10.1016/j.crme.2012.02.002 %G en %F CRMECA_2012__340_4-5_193_0
Graeme Walter Milton; Loc Hoang Nguyen. Bounds on the volume fraction of 2-phase, 2-dimensional elastic bodies and on (stress, strain) pairs in composites. Comptes Rendus. Mécanique, Volume 340 (2012) no. 4-5, pp. 193-204. doi : 10.1016/j.crme.2012.02.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.02.002/
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