Improving the reliability of material databases using
, M. Bonnet
, N. Carre
, F.-H. Leroy
, J.-F. Maire
Oﬃce National d’Etudes et Recherches Ae
rospatiales, 29 avenue de la division Leclerc, 92322 Cha
tillon Cedex, France
Laboratoire de Me
canique des Solides, CNRS UMR 7649, Ecole Polytechnique, 91128 Palaiseau Cedex, France
Received 14 May 2007; accepted 11 October 2007
Available online 13 November 2007
This article addresses the propagation of constitutive uncertainties between scales occurring in the multiscale modelling of ﬁbre-rein-
forced composites. The ampliﬁcation of such uncertainties through upward or downward transitions by a homogenisation model is
emphasized and exempliﬁed with the Mori–Tanaka model. In particular, the sensitivity to data uncertainty in the inverse determination
of constituent parameters based on downward transitions is stressed on an example. Then a database improvement method, which
exploits simultaneously the available information on constitutive uncertainties at all scales instead of just propagating those associated
with one scale, is presented and shown to yield substantial reductions in uncertainty for both the constitutive parameters and the
response of structures. The latter ﬁnding is demonstrated on two examples of structures, with signiﬁcant gains in conﬁdence obtained
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: A. Probabilistic methods; B. Mechanical properties; Computational mechanics
Over the past years, various homogenisation methods 
have been developed in order to determine the macroscopic
properties of a heterogeneous material from those of its
constituents. Among such materials, polymer–matrix com-
posites (PMCs) are a fundamental example of application
due to the various observation scales involved (constitu-
ents, elementary ply, laminate), the high elastic contrast
between their constituents (ﬁbre/matrix), and their inten-
sive and growing use in the aerospace industry.
However, except in few cases , multiscale modelling of
such materials has up to now been approached only from a
purely deterministic viewpoint. A set of material properties
at a small scale so determines precisely a corresponding set
of material properties at a larger scale. Therefore, most of
the time material properties are only known in a certain
range because of the inaccuracy of experimental methods
and the natural variability of the composite materials
induced by imperfectly controlled manufacturing processes.
The aim of this article is to evaluate the eﬀect of uncer-
tainties at a small scale on the ﬁnal properties at the larger
scales, and to propose a method based on multiscale tran-
sitions, referred to here as a database improvement
method, for reducing the uncertainties at the various scales.
The uncertainty propagation and ampliﬁcation along
scales is stressed in Section 2. The proposed database
improvement method is then presented in Section 3. The
conﬁdence gains aﬀorded by the proposed approach for
the analysis of composite structures are then demonstrated
in Section 4 on two examples, namely a hat-shaped compo-
nent under a three-points bending test, and the buckling of
0266-3538/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved.
Corresponding authors. Tel.: +33 (0) 146734661, +33 (0) 146734142;
fax: +33 381666700.
E-mail addresses: email@example.com (F.-H. Leroy), Jean-Francois.
Maire@onera.fr (J.-F. Maire).
Available online at www.sciencedirect.com
Composites Science and Technology 69 (2009) 73–80