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The overall elastic energy of polycrystalline martensitic solids

Bruno, Oscar P. and Reitich, Fernando and Leo, Perry H. (1996) The overall elastic energy of polycrystalline martensitic solids. Journal of the Mechanics and Physics of Solids, 44 (7). pp. 1051-1101. ISSN 0022-5096. http://resolver.caltech.edu/CaltechAUTHORS:20181101-152903698

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Abstract

We are concerned with the overall elastic energy in martensitic polycrystals. These are polycrystals whose constituent crystallites can undergo shape-deforming phase transitions as a result of changes in their stress or temperature. We approach the problem of calculation of the nonlinear overall energy via a statistical optimization method which involves solution of a sequence of linear elasticity problems. As a case study we consider simulations on a two-dimensional model in which circular randomly-oriented crystallites are arranged in a square pattern within an elastic matrix. The performance of our present code suggests that this approach can be used to compute the overall energies in realistic three-dimensional polycrystals containing grains of arbitrary shape. In addition to numerical results we present upper bounds on the overall energy. Some of these bounds apply to the square array mentioned above. Others apply to polycrystals containing circular, randomly-oriented crystallites with sizes ranging to infinitesimal, and no intergrain matrix. The square-array bounds are consistent with our numerical results. In some regimes they approximate them closely, thus providing an insight on the convergence of the numerical method. On the other hand, in the case of the random array the bounds carry substantial practical significance, since in this case the energy contains no artificial contributions from an elastic matrix. In all the cases we have considered our bounds compare favorably with those obtained under the well-known Taylor hypothesis; they show that, as far as polycrystalline martensite is concerned, calculations of the elastic energy based on the Taylor assumption may lead to substantial overestimates of this quantity.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/0022-5096(96)00031-2DOIArticle
ORCID:
AuthorORCID
Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 1996 Published by Elsevier. Received 24 October 1995. O.B. gratefully acknowledges support from NSF (through an NYI award and through grants No. DMS-9200002 and DMS-9523292), from the Sloan Foundation (through the fellowships program) from the Powell Research Foundation and from the AFOSR (contract No. F49620-96-1-0008). F.R. gratefully acknowledges support from AFOSR through grant No. F49620-95-1-0113. P.H.L. gratefully acknowledges support from NSF through grant CMS-9503393.
Funders:
Funding AgencyGrant Number
NSFDMS-9200002
NSFDMS-9523292
Alfred P. Sloan FoundationUNSPECIFIED
Charles Lee Powell FoundationUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)F49620-96-1-0008
Air Force Office of Scientific Research (AFOSR)F49620-95-1-0113
NSFCMS-9503393
Record Number:CaltechAUTHORS:20181101-152903698
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181101-152903698
Official Citation:Oscar P. Bruno, Fernando Reitich, Perry H. Leo, The overall elastic energy of polycrystalline martensitic solids, Journal of the Mechanics and Physics of Solids, Volume 44, Issue 7, 1996, Pages 1051-1101, ISSN 0022-5096, https://doi.org/10.1016/0022-5096(96)00031-2. (http://www.sciencedirect.com/science/article/pii/0022509696000312)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90586
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:02 Nov 2018 22:25
Last Modified:02 Nov 2018 22:25

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