Nonconvex energy functions. Hemivariational inequalities and substationarity principles. (English) Zbl 0538.73018

The purpose of the paper is the derivation of certain variational principles for material laws and boundary conditions resulting from nonconvex, nondifferentiable potentials. Two recently defined concepts of generalized gradient of Clarke [F. H. Clarke, Trans. Am. Math. Soc. 205, 247-262 (1975; Zbl 0307.26012)] and derivative container of Warga [J. Warga, Calc. Var. Control Theory, Proc. Symp. Math. Res. Cent., Madison 1975, 13-46 (1976; Zbl 0355.26004)] are employed. Hemivariational inequalities corresponding to discussed problems are derived.
Reviewer: W.Barański


74S30 Other numerical methods in solid mechanics (MSC2010)
74A20 Theory of constitutive functions in solid mechanics
49S05 Variational principles of physics
49J40 Variational inequalities
26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
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