Homogeneous equilibrium configurations of a hyperelastic compressible cube under equitriaxial dead-load tractions. (English) Zbl 1179.74012

Tarantino, Angelo Marcello

J. Elasticity 92, No. 3, 227-254 (2008).

This interesting and well-written paper is about a classical and important problem in nonlinear elasticity. The problem has been first stated by R. S. Rivlin [Philos. Trans. Roy. Soc. London, Ser. A 240, 459–508 (1948; Zbl 0029.32605)] in the framework of homogeneous deformations of a cube made of incompressible material and subject to equitriaxial dead-load tractions. In the present paper the original analysis has been extended to compressible neo-Hookean and Mooney-Rivlin materials. The authors consider the volumetric part of strain-energy function in a form that has been proposed by P. G. Ciarlet and G. Geymonat [C. R. Acad. Sci., Paris, Sér. II 295, 423–426 (1982; Zbl 0497.73017)] on the basis of mathematical arguments. This choice allows to accompany the analysis by beautiful plots and graphs that help to understand in a clear way what is going around with respect to non-uniqueness and stability of the solutions. This paper is of sure interest for researcher working in nonlinear elasticity. and clearly the next step is to consider the same problem when more realistic forms of the strain-energy function are in force.

Reviewer: Giuseppe Saccomandi (Lecce)

MSC:

74B20	Nonlinear elasticity
74G60	Bifurcation and buckling
74G35	Multiplicity of solutions of equilibrium problems in solid mechanics

Keywords:

bifurcation; stability; non-uniqueness; strain-energy function

Citations:

Zbl 0029.32605; Zbl 0497.73017

References:

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