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On abstract variational inequalities in viscoplasticity with frictional contact. (English) Zbl 1152.74030
From the summary: We study quasistatic abstract variational inequalities with time-dependent constraints. We prove existence results and present an approximation method valid for nonsmooth constraints. Then, we apply our results to the approximation of quasistatic evolution of an elastic body in bilateral contact with a rigid foundation. The contact involves viscous friction of Tresca or Coulomb type. We prove existence results for approximate problems and give a full asymptotic analysis, proving strong or weak convergence results.
74M15Contact (solid mechanics)
74M10Friction (solid mechanics)
74C10Small-strain, rate-dependent theories
74H10Analytic approximation of solutions for dynamical problems in solid mechanics
49J40Variational methods including variational inequalities
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