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Bounds on the Effective Elastic Properties of Martensitic Polycrystals

Bruno, Oscar P. and Reitich, Fernando (1998) Bounds on the Effective Elastic Properties of Martensitic Polycrystals. In: Mathematics of Multiscale Materials. IMA Volumes in Mathematics and its Applications. No.99. Springer , New York, NY, pp. 51-62. ISBN 978-1-4612-7256-4.

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We draw attention to the problem of estimation of elastic energies in martensitic polycrystals. In particular we introduce a tensorial parameter η=η_(ijkl) which contains information about the microgeometry and disorder of the polycrystalline structure. Under the assumption of isotropic elasticity and mild hypothesis on the statistics of the polycrystal, this parameter allows for explicit calculation of rigorous and stringent upper bounds on the effective energy. For circular grains in two dimensions η gives the elastic energy resulting from transformation of a single circular inclusion in an elastic matrix and the bounds coincide with those derived recently by Bruno, Reitich and Leo. Consideration of such particular cases shows that our bounds can yield substantial improvements over those obtained under Taylor’s constant strain hypothesis. For arbitrary microgeometries the statistical parameter η can be calculated by means of two-point correlations functions.

Item Type:Book Section
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Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 1998 Springer Science+Business Media New York. OB gratefully acknowledges support from NSF (through an NYI award and through contracts No. DMS-9200002 and DMS-9523292), from the Sloan Foundation (through the fellowships program), from the AFOSR (contract No. F49620-96-1-0008) and from the Powell Research Foundation. FR gratefully acknowledges support from AFOSR through grant No. F49620-95-1-0113 and from NSF through grant No. DMS-9622555.
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)F49620-96-1-0008
Charles Lee Powell FoundationUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)F49620-95-1-0113
Series Name:IMA Volumes in Mathematics and its Applications
Issue or Number:99
Record Number:CaltechAUTHORS:20181106-152204596
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90681
Deposited By: Tony Diaz
Deposited On:07 Nov 2018 21:19
Last Modified:16 Nov 2021 03:34

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