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Taylor expansions and bounds for the effective conductivity and the effective elastic moduli of multicomponent composites and polycrystals

Bruno, Oscar P. (1991) Taylor expansions and bounds for the effective conductivity and the effective elastic moduli of multicomponent composites and polycrystals. Asymptotic Analysis, 4 (4). pp. 339-365. ISSN 0921-7134. https://resolver.caltech.edu/CaltechAUTHORS:20181105-104502314

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Abstract

We describe a construction, based on variational inequalities, which gives a hierarchy of upper and lower bounds (of odd orders 2k+1), on the various effective moduli of random multiphase materials and polycrystals. The bounds of order 2k+1 on a given effective modulus can be explicitly evaluated if a truncated Taylor expansion of the given modulus is known to order 2k+1. Our approach is motivated by prior investigations of Beran and other authors. Our calculations do not involve Green functions or n-point correlation functions, and they are very simple. We thus rederive known and obtain new sequences of bounds on the different effective moduli. We also describe a method that, for cell materials (i.e. materials in which cells of smaller and smaller length scales cover all space, with material properties assigned at random), permits one to calculate the truncated Taylor expansions that are needed for the explicit evaluation of the bounds. In connection with this, we show that the first coefficient in the low volume fraction expansion of any effective modulus of a cell material, coincides with the corresponding low volume fraction coefficient for an array of cells randomly distributed in a matrix.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.3233/ASY-1991-4404DOIArticle
ORCID:
AuthorORCID
Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 1991 IOS Press, Inc. Received 4 April 1990.
Issue or Number:4
Record Number:CaltechAUTHORS:20181105-104502314
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181105-104502314
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90642
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Nov 2018 18:51
Last Modified:03 Oct 2019 20:27

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