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Weak solvability via bipotential method for contact models with nonmonotone boundary conditions. (English) Zbl 1327.74010

Summary: We consider a general mathematical model which describes the contact between a body and a foundation, under the small deformations hypothesis. The behavior of the material is modeled by a monotone constitutive law, while on the potential contact zone nonmonotone boundary conditions are imposed. We propose a variational formulation in terms of bipotentials, whose unknown is a pair consisting of the displacement field and the Cauchy stress field. The existence of weak solutions is proved using a recent result due to Costea and Varga (Topol Methods Nonlinear Anal 41:39-67, 2013) concerning the solvability of nonlinear hemivariational inequality systems.

MSC:

74A20 Theory of constitutive functions in solid mechanics
74M15 Contact in solid mechanics
49J40 Variational inequalities
49J53 Set-valued and variational analysis
35M87 Unilateral problems for mixed-type systems of PDEs and systems of variational inequalities with partial differential operators of mixed type
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