Analysis of a contact problem with normal damped response and unilateral constraint

作者：Barboteu Mikael; Danan David; Sofonea Mircea^*

来源：ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 2016, 96(4): 408-428.

DOI：10.1002/zamm.201400304

• Viscoelastic material
• frictional contact
• normal damped response
• unilateral constraint
• history-dependent quasivariational inequality
• weak solution
• finite element
• error estimate
• numerical simulations

We consider a mathematical model which describes the equilibrium of a viscoelastic body in frictional contact with an obstacle. The contact is modeled with normal damped response and unilateral constraint for the velocity field, associated to a version of Coulomb's law of dry friction. We present a weak formulation of the problem, then we state and prove an existence and uniqueness result of the solution. The proof is based on arguments of history-dependent quasivariational inequalities. We also study the dependence of the solution with respect to the data and prove a convergence result. Further, we introduce a fully discrete scheme to solve the problem numerically. Under certain solution regularity assumptions, we derive an optimal order error estimate of the discretization. Finally, we provide numerical simulations which illustrate the behavior of the solution with respect to the frictional contact conditions and validate the theoretical convergence results.

• 出版日期2016-4