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Stability of elastic material with negative stiffness and negative Poisson's ratio
Author(s) -
Xinchun Shang,
Lakes Roderic S.
Publication year - 2007
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200572719
Subject(s) - isotropy , poisson's ratio , stiffness , shear modulus , stability (learning theory) , cylinder , elastic modulus , mathematical analysis , materials science , physics , mathematics , poisson distribution , geometry , composite material , optics , statistics , machine learning , computer science
Stability of cuboids and cylinders of an isotropic elastic material with negative stiffness under partial constraint is analyzed using an integral method and Rayleigh quotient. It is not necessary that the material exhibit a positive definite strain energy to be stable. The elastic object under partial constraint may have a negative bulk modulus K and yet be stable. A cylinder of arbitrary cross section with the lateral surface constrained and top and bottom planar surfaces is stable provided the shear modulus G > 0 and – G /3 < K < 0 or K > 0. This corresponds to an extended range of negative Poisson's ratio, –∞ < ν < –1. A cuboid is stable provided each of its surfaces is an aggregate of regions obeying fully or partially constrained boundary conditions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)