Numéro |
J. Phys. IV France
Volume 105, March 2003
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Page(s) | 107 - 113 | |
DOI | https://doi.org/10.1051/jp4:20030177 |
J. Phys. IV France 105 (2003) 107
DOI: 10.1051/jp4:20030177
The modified affine homogenisation scheme for nonlinear composites: Comparison with variational bounds and estimates
R. Brenner1, O. Castelnau1 and P. Gilormini21 LPMTM, CNRS, Institut Galilée, Université Paris-Nord, 93430 Villetaneuse, France
2 LMT, ENS de Cachan, CNRS, Université Paris 6, 61 avenue du Président Wilson 94235 Cachan cedex, France
Abstract
The effective behaviour of heterogeneous materials exhibiting a random microstructure, such as
composites and polycrystals, can be efficiently estimated or bounded with homogenisation methods. For materials
with a nonlinear behaviour, use is classically made of a Linear Comparison Composite (LCC) presenting generally
the same microstructure as the nonlinear material, but for which the local (linearised) compliance is uniform per
phase. Homogenisation schemes, developed for linear behaviour, can thus be applied to the LCC. The way the LCC
is defined has a great influence on the estimated effective behaviour and local mechanical fields, in particular for
large nonlinearities and contrasts between the phases. For few years, it has become clear that not only the phase
averages of strain and stress must be used for defining the LCC, but also their intraphase fluctuations. In that
framework, the present authors have recently proposed a "modified affine" procedure [1] which presents the
advantage over other formulations to be applicable to any type of behaviour, including nonlinear viscoelasticity. In
this paper, we present a comparison, for simpler behaviour (nonlinear elasticity), between the proposed approach
and several formulations previously proposed in the literature.
© EDP Sciences 2003