Necessary and sufficient criteria for ellipticity of the equilibrium equations of a nonlinearly elastic medium
type: Item
instance of: scholarly article
title: Necessary and sufficient criteria for ellipticity of the equilibrium equations of a nonlinearly elastic medium
zbMATH Open document ID: 0905.73012
DOI: 10.1016/0021-8928(95)00023-I
author: A. N. Rudev
author: L. M. Zubov
published in: Journal of Applied Mathematics and Mechanics
publication date: 1997-11-03T00:00:00Z
review text: The necessary and sufficient conditions for ellipticity of the equilibrium equations of a nonlinear elastostatics are obtained in terms of constraints on the strain-energy function and on the principal elongations. In particular, to get an elliptic elasticity theory, the strain energy and elongations are to comply with a number of algebraic inequalities subject to constant-sign polynomial conditions. The results cover the case of an arbitrary anisotropic elastic body, and for particular material symmetries reduce to those discussed before by: (i) \textit{L. Zee} and \textit{E. Sternberg} [Arch. Ration. Mech. Anal. 83, 53-90 (1983; Zbl 0553.73011); (ii) \textit{P. K. Blatz} and \textit{W. L. Ko} [Trans. Soc. Rheol. 6, 223-251 (1962)]; and (iii) \textit{M. Baker} and \textit{J. L. Ericksen} [J. Washington Acad. Sci. 44, No. 2, 33-35 (1954)].
reviewed by: Józef Ignaczak
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 35Q72
zbMATH DE Number: 1077477
zbMATH Keywords: strain-energy function
zbMATH Keywords: principal elongations
zbMATH Keywords: algebraic inequalities
zbMATH Keywords: constant-sign polynomial conditions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1077477