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Conditions for the Division of the Deviator and Spherical Properties for Nonlinear Isotropic Tensor Functions

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Abstract

For isotropic elastic continuous media, we consider a class of tensor nonlinear constitutive relations connecting stresses with small strains and including three material functions from any triple of independent invariants. General conditions are derived for these material functions, under which the deviatory and spherical properties of the tensor function defining the operator of the constitutive relations are not related to each other. These conditions are narrowed if the medium has a scalar potential, as well as if tensor linearity is additionally required. In the latter case, possible parametrizations of the stress and strain deviators and their representations in five-dimensional vector spaces are given.

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Funding

This work was supported by the Russian Science Foundation, grant no. 22-21-00077.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    D. V. Georgievskii

  2. Ishlinskii Institute for Problems in Mechanics, Moscow, Russia

    D. V. Georgievskii

  3. Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia

    D. V. Georgievskii

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

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Georgievskii, D.V. Conditions for the Division of the Deviator and Spherical Properties for Nonlinear Isotropic Tensor Functions. Dokl. Phys. 67, 165–168 (2022). https://doi.org/10.1134/S1028335822060052

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  • DOI: https://doi.org/10.1134/S1028335822060052

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