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


Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

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.

About the authors

D.V. Georgievskii

Lomonosov Moscow State University; Ishlinsky Institute for Problems in Mechanics RAS

Author for correspondence.
Email: georgiev@mech.math.msu.su
Russian Federation, Leninskie Gory 1, Moscow, 119992; pr. Vernadskogo 101, str. 1, Moscow, 119526

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2018 Allerton Press, Inc.