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Non-polyconvexity of the stored energy function of a Saint Venant- Kirchhoff material. (English) Zbl 0608.73023

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.

MSC:

74B20 Nonlinear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)
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References:

[1] J. Ball: Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal. 63 (1977), p. 337-403. · Zbl 0368.73040 · doi:10.1007/BF00279992
[2] P. G. Ciarlet: Lectures on three-dimensional elasticity. Tata Institute Lecture Notes, Springer- Verlag, 1983. · Zbl 0542.73046
[3] P. G. Ciarlet: Topics in mathematical elasticity, vol. I. North-Holland, Amsterdam, 1985.
[4] J. Nečas: Introduction to the theory of nonlinear equations. Teubner Texte für Mathematik, Band 52, Leipzig.
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