The Relationship between Auxetic and Negative Stiffness Materials Behavior. Part I: Theory

V. Chiroiu(1*), L. Munteanu(2), D. Dumitriu(3)

(1) Institute of Solid Mechanics of Romanian Academy, Romania
(2) Institute of Solid Mechanics of Romanian Academy, Romania
(3) Institute of Solid Mechanics of Romanian Academy, Romania
(*) Corresponding author

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The purpose of the paper is to study the relationship between the behavior of auxetic and negative stiffness materials. These materials are modeled as chiral Cosserat media. The classical mechanics fails when describes the behavior of auxetic and negative stiffness materials, because these materials exhibit chiral effects and non-affine deformations. A new architecture for a cellular elastic solid with a chess board structure composed from auxetic materials of positive and negative stiffness, is proposed. The characterization of the cellular solid with the calculation of material constants will be presented in the forthcoming paper.
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Auxetic Material; Negative Poisson’ratio; Negative Stiffness Material; Chess Board Structure

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P. Rosakis, A. Ruina, R. S. Lakes, Microbuckling instability in elastomeric cellular solids, J. Materials Science, Vol. 28, pp.4667–4672, 1993.

R. S. Lakes, Experimental micromechanics methods for conventional and negative Poisson's ratio cellular solids as Cosserat continua, J. Engineering Materials and Technology, Vol. 113, pp.148–155, 1991.

R. S. Lakes, Foam structures with a negative Poisson's ratio, Science, Vol. 235, pp.1038–1040, 1987.

R. S. Lakes, Experimental Microelasticity of Two Porous Solids, Int. J. Solids, Structures, Vol. 22, pp.55–63, 1986.

A.E.H. Love, A treatise on the mathematical theory of elasticity (4th ed., Dover, New York, 1926).

Y. C. Wang, R. S. Lakes, A. Butenhoff, Cellular Polymers, Vol.20, pp.373–385, 2001.

R. S. Lakes, Extreme damping in compliant composites with a negative stiffness phase, Philos. Mag. Lett., Vol.81, 95–100, 2001.

R. S. Lakes, Extreme damping in composite materials with a negative stiffness phase, Phys. Rev. Lett., Vol.86, 13, pp.2897–2900, 2001.

S. Sandler, J.P. Wright, Theoretical foundation for large scale computations of nonlinear material behavior, (eds. S. Nemat Nasser, R. J. Asarom G. A. Hegemier, M. Nijhoff, 1984).

V. Chiroiu, L. Munteanu, D. Dumitriu, M. Beldiman, C. Secara, On the theory of materials with negative stiffness components, Journal of Optoelectronics and Advanced Materials (JOAM), Vol.10, nr.3, 2008.

R. S. Lakes, T. Lee, A. Bersie, Y. C. Wang, Extreme damping in composite materials with negative stiffness inclusions, Nature, Vol.410, pp.565–567, 2001.

R. S. Lakes, W. J. Drugan, Dramatically stiffer elastic composite materials due to a negative stiffness phase?, J. of the Mechanics and Physics of Solids, Vol.50, pp.979–1009, 2002.

R. D. Gauthier, Experimental investigations on micropolar media, Mechanics of Micropolar Media, CISM Courses and lectures (edited by O. Brulin and R.K.T. Hsieh, World scientific, 1982, pp.395–463).

P.P.Teodorescu, L. Munteanu, V. Chiroiu, On the wave propagation in chiral media, New Trends in Continuum Mechanics, Theta Series in Advanced Mathematics (ed. M.Mihailescu-Suliciu, Editura Theta Foundation, Bucuresti, 2005, pp.303–310).

P.P.Teodorescu, T. Badea, L. Munteanu, J. Onisoru, On the wave propagation in composite materials with a negative stiffness phase, New Trends in Continuum Mechanics, Theta Series in Advanced Mathematics (ed. M.Mihailescu-Suliciu Ed. Theta Foundation, Bucharest, 2005, pp.295–302).

E. and F. Cosserat, Theorie des Corps Deformables (Hermann et Fils, Paris, 1909).

R. D. Mindlin, Microstructure in linear elasticity, Arch. Rat. Mech. Anal., Vol.16, pp.51–78, 1964.

R. D. Mindlin, Stress functions for a Cosserat continuum, Int J. Solids Structures, Vol.1, pp.265–271, 1965.

A. C. Eringen, Linear Theory of Micropolar Elasticity, J. Math. & Mech., Vol.15, pp.909–924, 1966.

A. C. Eringen, Theory of micropolar elasticity, Fracture, 2 (ed. R. Liebowitz, Academic Press, 1968, pp.621–729).

A. C. Eringen, Theory of micropolar fluids, J. Math. Mech., Vol.16, pp.1–18, 1966.

R. S. Lakes, R. L. Benedict, Noncentrosymmetry in micropolar elasticity, Int. J. Engng. Sci., Vol.20, n.10, 1161–1167, 1982.

A. F. Jankowski, T. Tsakalakos, T., The effect of strain on the elastic constants of noble metals, J. Phys. F: Met. Phys., Vol.15, pp.1279–1292, 1985.

A. F. Jankowski, Modelling the supermodulus effect in metallic multilayers, J. Phys. F: Met. Phys., Vol.18, pp.413–427, 1988.

P. P. Delsanto, V. Provenzano, H. Uberall, Coherency strain effects in metallic bilayers, J. Phys.: Condens. Matter, Vol.4, pp.3915–3928, 1992.

L. V. Berlyand, S. M. Kozlov, Asymptotic of the homogenized moduli for the elastic chess-board composite, Arch. Rational Mech., Anal., Vol.118, pp.95–112, 1992.

R. A. Toupin, B. Bernstein, B., Sound waves in deformed perfectly elastic materials, Acoustoelastic effect, J. Acoust. Soc. Am., Vol.33, n.2, pp.216–225, 1961.

J. D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion and related problem, Proc. Royal Soc., Vol.A241, pp.376–396, 1957.

D. Baral, J. E. Hilliard, J. B. Jetterson, K. Miyano, Determination of the primary elastic constants from thin foils having a strong texture, J. Appl., Phys. Vol.53, n.5, 1982


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