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Quasistatic frictional problems for elastic and viscoelastic materials. (English) Zbl 1090.74041
An approach to quasistatic frictional problems whose variational formulations include a subspace as a set of admissible functions is presented. The approach is suitable for the evolution problems of the normal-compliance type as well as for the homogeneous Dirichlet boundary condition (sometimes considered as a two-sided contact problem) if possible acceleration is neglected. The existence and uniqueness of solutions is proved for both viscoelastic and purely elastic materials. The convergence of solutions of the viscoelastic problems to the solution of the elastic one for the vanishing viscosity is proved as well. At the end, a list of several models solvable by the approach is added. A possible modification or limit to unilateral contact conditions (respecting in particular the freedom of the body to move from the obstacle) is not considered.
MSC:
74M10Friction (solid mechanics)
74D05Linear constitutive equations (materials with memory)
58E35Variational inequalities (global problems)
35J65Nonlinear boundary value problems for linear elliptic equations