Abstract
Based on the apparatus of tensor functions of one tensor arg ument, a multilevel family of scalar stress potentials with respect to deformations of isotropic elastic media is proposed, in which the elements of each level include elements of all previous levels. This potential generates a multilevel family of tensorially nonlinear constitutive relations in which each term, regardless of the level, has the first order of smallness in terms of the tendency of the deformation norm to zero. The number of material constants included in the multilevel constitutive relations is found. A system of installation experiments is proposed for finding four material constants in direct and inverse ratios of the second level. The questions of the reciprocity of tensor functions and the positive definiteness of the second-level potential, which leads to a tensor-linear dependence of stresses on strains, are discussed.
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This work was supported by the Russian Science Foundation (project no. 22-21-00077).
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Translated by I. K. Katuev
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Georgievskii, D.V. Isotropic Tensor Functions with Quasipolynomial Scalar Potential in Nonlinear Elasticity Theory. Mech. Solids 57, 1359–1364 (2022). https://doi.org/10.3103/S0025654422060231
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DOI: https://doi.org/10.3103/S0025654422060231