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Stability criteria for continuous and discrete elastic composites and the influence of geometry on the stability of a negative-stiffness phase

Kochmann, Dennis M. (2012) Stability criteria for continuous and discrete elastic composites and the influence of geometry on the stability of a negative-stiffness phase. Physica Status Solidi B, 249 (7). pp. 1399-1411. ISSN 0370-1972 . http://resolver.caltech.edu/CaltechAUTHORS:20120810-140037087

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Abstract

Recent experimental findings and theoretical analyses have confirmed the bound-exceeding performance of composite materials with one constituent of so-called negative stiffness (i.e., with non-positive-definite elastic moduli): the overall elastic properties greatly exceed those of the composite constituents, when the negative-stiffness phase's properties are appropriately tuned. However, the stability of such composite materials has remained a key open question. It has been shown, e.g., that a spherical particle of a negative-stiffness material can be stabilized when embedded in a sufficiently stiff and thick coating to impose a geometrical constraint on the negative-stiffness phase. For general composite geometries (as those arising from actual manufacturing processes), no such investigation has been reported. We review the classical stability conditions for homogeneous linear elastic solids and outline methods to determine the sufficient stability conditions for elastic composites. In addition, a numerical technique to obtain the stability restrictions on the elastic moduli of a composite with, in principle, arbitrary geometry is presented. Based on this method, we investigate the stability of simple elastic two-phase composites consisting of an inclusion (having non-positive-definite elastic moduli) embedded in a different coating material. In particular, the influence of the geometry of the encapsulated particles and the surrounding matrix is shown to considerably affect the overall stability. Our results compare the stability limits for two- (2D) and three-dimensional (3D) composite arrangements and provide design guidelines for optimal stability.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/pssb.201084213DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/pssb.201084213/abstractPublisherArticle
ORCID:
AuthorORCID
Kochmann, Dennis M.0000-0002-9112-6615
Additional Information:© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. Received 27 September 2010, revised 11 January 2012, accepted 2 February 2012. Published online 19 March 2012. The author thanks W. J. Drugan and K. Hackl for fruitful discussions, and C. Hecht for computational work.
Group:GALCIT
Subject Keywords:composites, finite element method, linear elasticity, negative stiffness, stability
Record Number:CaltechAUTHORS:20120810-140037087
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120810-140037087
Official Citation:Kochmann, D. M. (2012), Stability criteria for continuous and discrete elastic composites and the influence of geometry on the stability of a negative-stiffness phase. Phys. Status Solidi B, 249: 1399–1411. doi: 10.1002/pssb.201084213
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33103
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:10 Aug 2012 22:55
Last Modified:14 Sep 2016 00:01

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