Abstract
Based on the choice of two physically meaningful strain measures, we study necessary and sufficient conditions for strong ellipticity of the equilibrium equations for two-dimensional isotropic hyperelastic bodies. Specifically, we show, depending on the values of the derivatives of the energy function, that strong ellipticity is equivalent to a single condition with a clear physical interpretation.
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Notes
Lin+ denotes the set of second order tensors on ℝ2 with positive determinant.
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Acknowledgements
The authors have been supported by MIUR-PRIN 2008, ‘Modelli multiscala per strutture in materiali innovativi’ and by Progetto di ricerca industriale-Regione Puglia, ‘Modelli innovativi per sistemi meccatronici’.
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De Tommasi, D., Puglisi, G. & Zurlo, G. A Note on Strong Ellipticity in Two-Dimensional Isotropic Elasticity. J Elast 109, 67–74 (2012). https://doi.org/10.1007/s10659-011-9370-1
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DOI: https://doi.org/10.1007/s10659-011-9370-1