Conditions necessaires de faible fermeture et de 1-rang convexity en dimension 3. (Necessary conditions for weak closure and rank-one convexity in three-dimensional elasticity). (French) Zbl 0647.73017

Aubert, G.; Tahraoui, R.

Rend. Circ. Mat. Palermo, II. Ser. 34, 460-488 (1985).

In this interesting paper, motivated by minimization problems of nonlinear isotropic elasticity, authors study certain necessary conditions of sequentially weak closure for the domain where the candidate minimizers are sought; these conditions have the form of kinematical constraints on admissible stretches. Moreover, for rank-one convex stored energy functions of class \(C^ 2\), necessary conditions are found whose constitutive significance would perhaps deserve further investigation.

Reviewer: P.Podio-Guidugli

MSC:

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

Keywords:

isotropic regular functions; restricted convexity; minimization problems; isotropic elasticity; sequentially weak closure; kinematical constraints on admissible stretches; rank-one convex stored energy functions

References:

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