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Analytical stability conditions for elastic composite materials with a non-positive-definite phase

Kochmann, D. M. and Drugan, W. J. (2012) Analytical stability conditions for elastic composite materials with a non-positive-definite phase. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 468 (2144). pp. 2230-2254. ISSN 1364-5021. http://resolver.caltech.edu/CaltechAUTHORS:20120801-093547662

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Abstract

Elastic multi-phase materials with a phase having appropriately tuned non-positive-definite elastic moduli have been shown theoretically to permit extreme increases in multiple desirable material properties. Stability analyses of such composites were only recently initiated. Here, we provide a thorough stability analysis for general composites when one phase violates positive-definiteness. We first investigate the dynamic deformation modes leading to instability in the fundamental two-phase solids of a coated cylinder (two dimensions) and a coated sphere (three dimensions), from which we derive closed-form analytical sufficient stability conditions for the full range of coating thicknesses. Next, we apply the energy method to derive a general correlation between composite stability limit and composite bulk modulus that enables determination of closed-form analytical sufficient stability conditions for arbitrary multi-phase materials by employing effective modulus formulas coupled with a numerical finite-element stability analysis. We demonstrate and confirm this new approach by applying it to (i) the two basic two-phase solids already analysed dynamically; and (ii) a more geometrically complex matrix/distributed-inclusions composite. The specific new analytical stability results, and new methods presented, provide a basis for creation of novel, stable composite materials.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1098/rspa.2011.0546 DOIArticle
http://rspa.royalsocietypublishing.org/content/468/2144/2230PublisherArticle
ORCID:
AuthorORCID
Kochmann, D. M.0000-0002-9112-6615
Additional Information:© 2012 The Royal Society. Received 9 September 2011. Accepted 15 February 2012. Published online before print March 14, 2012. This research was supported by the National Science Foundation (NSF) under grant DMR-0949254, and the Army Research Office/Defense Advanced Research Projects Agency (ARO/DARPA) under grant 57492-EG-DRP.
Group:GALCIT
Funders:
Funding AgencyGrant Number
NSFDMR-0949254
Army Research Office (ARO)57492-EG-DRP
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Subject Keywords:stability; elasticity; composite material; negative stiffness
Record Number:CaltechAUTHORS:20120801-093547662
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120801-093547662
Official Citation:D. M. Kochmann and W. J. Drugan Analytical stability conditions for elastic composite materials with a non-positive-definite phase Proc. R. Soc. A August 8, 2012 468 2230-2254; published ahead of print March 14, 2012, doi:10.1098/rspa.2011.0546
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32828
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:01 Aug 2012 16:50
Last Modified:14 Sep 2016 00:01

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