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Raoult, Annie
Non-polyconvexity of the stored energy function of a Saint Venant-Kirchhoff material. (English). Aplikace matematiky, vol. 31 (1986), issue 6, pp. 417-419
MSC: 73G10, 74B20, 74S30 | MR 0870478 | Zbl 0608.73023 | DOI: 10.21136/AM.1986.104220
Keywords:
non-polyconvexity; stored energy function; Saint Venant-Kirchhoff material; counter-example
Summary:
A direct proof of the non-polyconvexity of the stored energy function of a Saint Venant-Kirchhoff material is given by means of a simple counter-example.
References:
[1] J. Ball: Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal. 63 (1977), p. 337-403. DOI 10.1007/BF00279992 | MR 0475169 | Zbl 0368.73040
[2] P. G. Ciarlet: Lectures on three-dimensional elasticity. Tata Institute Lecture Notes, Springer- Verlag, 1983. MR 0730027 | Zbl 0542.73046
[3] P. G. Ciarlet: Topics in mathematical elasticity, vol. I. North-Holland, Amsterdam, 1985. MR 0936420
[4] J. Nečas: Introduction to the theory of nonlinear equations. Teubner Texte für Mathematik, Band 52, Leipzig.
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