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Unilateral problems in continuum mechanics. (English) Zbl 0645.73045
Material instabilities in continuum mechanics, Proc. Symp. Edinburgh/Scotl. 1985/86, 495-503 (1988).
[For the entire collection see Zbl 0627.00023.]
The aim of this paper is to extend and unify some well known results on noncoercive variational inequalities due to Fichera and to Lions and Stampacchia [e.g. G. Stampacchia, Actes Congr. Internat. Math. 1970, 2, 877-883 (1971; Zbl 0241.35001)]. The well-known classical results by Fichera and Lions and Stampacchia for the minimization of quadratic functionals on convex subsets of Hilbert space are extended in the framework of nonlinear elasticity (the poly-convex elastic energy functionals, materials reacting elastically to compression but not to traction - the masonry-like materials).
Reviewer: J.Lovíšek

MSC:
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
49J27 Existence theories for problems in abstract spaces
74B20 Nonlinear elasticity
49J40 Variational inequalities
58E25 Applications of variational problems to control theory