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Viscoplasticity with frictional contact and rapid growth
Author(s) -
Gleń Łukasz
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3761
Subject(s) - quasistatic process , monotone polygon , dissipation , mathematics , viscoplasticity , nonlinear system , mathematical analysis , deformation (meteorology) , monotonic function , classical mechanics , constitutive equation , geometry , physics , finite element method , quantum mechanics , meteorology , thermodynamics
We consider a problem in the inelastic deformation theory with a quasistatic deformation process of the gradient‐monotone type. We assume that the body has contact with a rigid foundation: the body moves on the foundation with friction. The frictional contact is modelled by a velocity‐dependent dissipation functional. This makes an evolution problem with two nonlinear monotone operators. We consider the gradient‐monotone inelastic constitutive function with a rapid growth at infinity. This leads us to a nonreflexive Orlicz space as an operational base. The frictional dissipation potential brings about a minimalization problem in this nonreflexive Orlicz space. Copyright © 2016 John Wiley & Sons, Ltd.