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Published August 8, 2012 | public
Journal Article

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


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.

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.

Additional details

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October 18, 2023