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An Order of Smallness of the Poynting Effect from the Standpoint of the Tensor Nonlinear Functions Apparatus

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Abstract

A class of constitutive relations is considered that connect symmetric stress and small strain tensors in three-dimensional space using an isotropic potential tensor nonlinear function of a rather general form. Various definitions of tensor nonlinearity are given and their equivalence is shown. From the standpoint of the mathematical apparatus of the theory of tensor nonlinear functions, the interpretation of the Poynting effect known in experimental mechanics and similar phenomena has been carried out. It is proved that these effects are not necessarily the result of the tensor nonlinearity of the defining relations, but may be due to the dependence on one of the material functions on the quadratic invariant, which is absent, for example, in the physically linear case. From here conclusions are drawn about the order of smallness of these effects. The possibility of modeling the Poynting effect by tensor-linear defining relations is discussed.

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Acknowledgments

The study was carried out in the frameworks of the state task (state registration number AAAA-A17-117021310373-3).

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Authors and Affiliations

  1. Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119992, Russia

    D.V. Georgievskii

  2. Ishlinsky Institute for Problems in Mechanics RAS, pr. Vernadskogo 101, str. 1, Moscow, 119526, Russia

    D.V. Georgievskii

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  1. D.V. Georgievskii
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Correspondence to D.V. Georgievskii.

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Original Russian Text © D.V. Georgievskii, 2018, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2018, No. 4, pp. 29–33.

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Georgievskii, D. An Order of Smallness of the Poynting Effect from the Standpoint of the Tensor Nonlinear Functions Apparatus. Mech. Solids 53, 381–384 (2018). https://doi.org/10.3103/S0025654418040039

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