Mechanics & Industry
Volume 18, Number 2, 2017
|Number of page(s)||5|
|Published online||17 February 2017|
Towards improved Hashin–Shtrikman bounds on the effective moduli of random composites
UniversitéParis-Est, Laboratoire Navier, ENPC, IFSTTAR, CNRS UMR 8205, 6 et 8 avenue Blaise Pascal, 77455 Marne-la-Vallée Cedex 2, France
a Corresponding author: email@example.com
Received: 7 December 2015
Accepted: 4 July 2016
The celebrated bounds of Hashin and Shtrikman on the effective properties of composites are valid for a very wide class of materials. However, they incorporate only a very limited amount of information on the microstructure (volume fraction of each phase in the case of isotropic microstructures). As a result, they are generally not tight. In this work, we present an attempt at improving these bounds by incorporating explicitly the local volume fraction to the set of local descriptors of the microstructure. We show that, quite unexpectedly, the process fails in the sense that the classical bounds are retrieved. We further show that this negative result applies to so-called weakly isotropic local descriptors of the microstructure (to be defined in this paper). This suggests that improved bounds may be obtained with anisotropic descriptors.
Key words: Elasticity / homogenization / bounds / effective properties / local volume fraction
© AFM, EDP Sciences 2017
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.