Abstract
It is shown that the medium exhibiting the property of boundedness for normal stresses is hyperelastic, and the constitutive equation of the medium model is a nonlinear relation between the Piola–Kirchhoff and Green–Saint–Venant tensors. For an isotropic medium, it is shown that the stress and strain tensors are coaxial, and a representation of the relation between the stress and strain tensors in the form of elementary functions of a tensor argument is obtained. A geometric proof of the uniqueness of the obtained representation is given.
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Original Russian Text © A.I. Glushko, I.I. Neshcheretov, 2018, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2018, No. 6, pp. 129–144.
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Glushko, A.I., Neshcheretov, I.I. Construction of Models for Elastic Media with the Restricted Normal Components of the Stress Vector. Mech. Solids 53, 707–720 (2018). https://doi.org/10.3103/S0025654418060122
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DOI: https://doi.org/10.3103/S0025654418060122