A mixed variational problem with applications in contact mechanics

作者：Sofonea Mircea^*; Matei Andaluzia

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2015, 66(6): 3573-3589.

DOI：10.1007/s00033-015-0573-3

• Mixed variational problem
• Lagrange multiplier
• History-dependent operator
• Frictionless contact
• Normal compliance
• Unilateral constraint
• Weak solution

We provide an existence result in the study of an abstract mixed variational problem which involves a history-dependent operator and two nondifferentiable functionals depending on the solution. The proof relies on generalized saddle point theory and a fixed point argument. Then we consider a new mathematical model which describes the quasistatic frictionless contact process between a viscoplastic body and an obstacle. The contact is modeled with a multivalued normal compliance condition and unilateral constraint. We use our abstract result to prove the weak solvability of this contact problem.

• 出版日期2015-12