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Solvability of a quasi-steady rolling problem for porous materials. (English) Zbl 1290.74029

Summary: A quasi-steady rolling problem with nonlocal friction, for porous rigid-plastic, strain-rate-sensitive and strain hardening materials, is considered. A variational formulation is derived, consisting of a variational inequality and two evolution equations, coupling the velocity, strain hardening and relative density variables. The convergence of a variable stiffness parameters method is proved, and existence and uniqueness results are obtained. An algorithm, combining this method with the finite element method, is proposed and used for solving an illustrative rolling problem.

MSC:

74M10 Friction in solid mechanics
74M15 Contact in solid mechanics
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
49J40 Variational inequalities
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