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Hemivariational inequalities for linear and nonlinear elastic materials. (English) Zbl 0657.73014

The paper presents several examples of nonmonotone and multivalued boundary conditions arising in the modern theory of continuum mechanics. Such conditions result in a lack of convexity, yet weak (variational) formulations are available in the form of hemivariational inequalities. Physically linear and nonlinear elastic problems are studied. Several hemivariational inequalities are formulated and investigated. For linear plane elasticity (i.e., two-dimensional case) the existence theorem is proven by means of mollifier regularization technique and Galerkin approximation method. Two numerical examples are presented and compared with known analytical solutions. One of them is an adhesive contact problem of two coaxial cylinders and the other concerns the beam lying on an adhesive foundation.
The reader interested in hemivariational inequalities in continuum mechanics should refer to the other papers by the first author [e.g.: CISM Courses Lect. 288, 223-246 (1985; Zbl 0621.49003); Z. Angew. Math. Mech. 65, 29-36 (1985; Zbl 0574.73015); Inequality problems in mechanics and applications. Convex and nonconvex energy functions (1985; Zbl 0579.73014); Topics in nonsmooth mechanics, 75-142 (1988; Zbl 0655.73010); C. R. Acad. Sci., Paris, Sér. I 307, No.13, 735-738 (1988; Zbl 0653.73011)].
Reviewer: W.R.Bielski

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74B20 Nonlinear elasticity
49J40 Variational inequalities
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
49M15 Newton-type methods
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