In an analysis presented in 1909, Poynting (page 546 of [1]) had shown that for finite elastic deformations, the lines of greatest extension and contraction are inclined to the diagonals of the rhombus into which a square is sheared. The implication of this finding was that when slender structures are twisted, they undergo elongation as experimentally verified by Poynting's measurements with wires [1]. While many theoretical analyses have shown the possibility of Poynting and reverse (inverse) Poynting effect [2-7], measurements of such effects are rather sparse [8-11]. We present here measurements of a highly nonlinear Poynting effect, including its reversal from positive to negative (elongation to compression) direction during torsion. Such atypical behavior is exhibited by a rather exceptional material system that has a pantographic internal structure. For this material system, the classical Cauchy-type continuum model fails and a 2nd gradient continuum model is necessary to describe many of its deformation behaviors.

Pantographic metamaterials show atypical Poynting effect reversal

Giorgio, Ivan;dell'Isola, Francesco
2018

Abstract

In an analysis presented in 1909, Poynting (page 546 of [1]) had shown that for finite elastic deformations, the lines of greatest extension and contraction are inclined to the diagonals of the rhombus into which a square is sheared. The implication of this finding was that when slender structures are twisted, they undergo elongation as experimentally verified by Poynting's measurements with wires [1]. While many theoretical analyses have shown the possibility of Poynting and reverse (inverse) Poynting effect [2-7], measurements of such effects are rather sparse [8-11]. We present here measurements of a highly nonlinear Poynting effect, including its reversal from positive to negative (elongation to compression) direction during torsion. Such atypical behavior is exhibited by a rather exceptional material system that has a pantographic internal structure. For this material system, the classical Cauchy-type continuum model fails and a 2nd gradient continuum model is necessary to describe many of its deformation behaviors.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/123389
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