A viscoplastic contact problem with a normal compliance with limited penetration condition and history-dependent stiffness coefficient. (English) Zbl 1273.74364
Summary: We consider a mathematical model that describes frictionless contact between a viscoplastic body and a deformable obstacle or foundation. The process is quasistatic and contact is modeled with the normal compliance with limited penetration condition, which has been introduced recently. Moreover, the contact stiffness coefficient is allowed to depend on the history of the contact process. We derive a variational formulation of the problem, which is in the form of a strongly nonlinear system coupling an integral equation and a time-dependent variational inequality. Then, we provide the analysis of the problem, which includes its unique weak solvability and the continuous dependence of the solution on the problem data. The proofs are based on results from the theory of history-dependent variational inequalities, on monotonicity and a fixed point argument.
MSC:
| 74M15 | Contact in solid mechanics |
| 35J87 | Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators |
| 49J40 | Variational inequalities |
| 74D10 | Nonlinear constitutive equations for materials with memory |
Keywords:
frictionless contact; normal compliance with limited penetration condition; history-dependent variational inequality; weak solution; continuous dependenceReferences:
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