Pantographic Metamaterials Show Atypical Poynting Effect Reversal

Anil Misra (1, 2, 3) , Tomasz Lekszycki (4) , Ivan Giorgio (2, 5, 3) , Gregor Ganzosch (6) , Wolfgang H. Müller (6) , Francesco Dell'Isola (2, 5, 3)

1 University of Kansas [Kansas City]
2 M&MoCS - International Research Centre on Mathematics & Mechanics of Complex Systems
3 Research Institute for Mechanics, National Research Lobachevsky State University of Nizhni Novgorod, Russia
4 Faculty of Mechanical and Engineering Production
5 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
6 Institute for Mechanics, TU Berlin, Germany

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 0002; 0003; 0004; 0005; 0006 ; 0007, measurements of such effects are rather sparse 0008; 0009; 0010 ; 0011. 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.

Domaines: Mécanique [physics]

Anil Misra, Tomasz Lekszycki, Ivan Giorgio, Gregor Ganzosch, Wolfgang H. Müller, et al.. Pantographic Metamaterials Show Atypical Poynting Effect Reversal. Mechanics Research Communications, 2018, ⟨10.1016/j.mechrescom.2018.02.003⟩. ⟨hal-01724940⟩