On Ellipticity of Hyperelastic Models Based on Experimental Data

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Abstract


The condition of ellipticity of the equilibrium equation plays an important role for correct description of mechanical behavior of materials and is a necessary condition for new defining relationships. Earlier, new deformation measures were proposed to vanish correlations between the terms, that dramatically simplifies restoration of defining relationships 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.

About the authors

V Yu Salamatova

Moscow Institute of Physics and Technology (State University) ; Sechenov First Moscow State Medical University

Email: salamatova@gmail.com
9 Institutskiy per., 141701 Moscow Region, Russia; 2 build. 4 Bol’shaya Pirogovskaya st., 119991 Moscow, Russia

Yu V Vasilevskii

Institute of Numerical Mathematics of the Russian Academy of Sciences ; Moscow Institute of Physics and Technology (State University) ; Sechenov First Moscow State Medical University

Email: yuri.vassilevski@gmail.com
8 Gubkina st., 119333 Moscow, Russia; 9 Institutskiy per., 141701 Moscow Region, Russia;2 build. 4 Bol’shaya Pirogovskaya st., 119991 Moscow, Russia

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