Abstract
The condition of ellipticity of the equilibrium equation plays an important role for the correct description of the mechanical behavior of materials and is a necessary condition for new constitutive relations. Earlier, new deformation measures were proposed to remove correlations between the terms, which dramatically simplifies restoration of constitutive relations from experimental data. One of these new deformation measures is based on the QR-expansion of deformation gradient. In this paper, we study the strong ellipticity condition for hyperelastic material using the QR-expansion of deformation gradient.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 63, No. 3, Differential and Functional Differential Equations, 2017.
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Salamatova, V.Y., Vasilevskii, Y.V. On Ellipticity of Hyperelastic Models Restored by Experimental Data. J Math Sci 253, 720–729 (2021). https://doi.org/10.1007/s10958-021-05264-y
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DOI: https://doi.org/10.1007/s10958-021-05264-y