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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.

MSC:

74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
49J40 Variational inequalities
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