Frictional contact problems with normal compliance. (English) Zbl 0662.73079
The quasistatic problem of a linear elastic body in unilateral contact with a rigid support subject to Coulomb’s friction law and a power law normal compliance is considered. Two approximations are derived. It is proved that the first, the incremental problem, possesses a solution but it is unique only if it is small and the coefficient of friction is small enough. It is suitable for numerical calculations. The second, the rate problem, captures exactly the path dependence of the quasistatic problem, is more suitable for theoretical investigations and possesses a unique solution for “small” coefficients.
MSC:
| 74A55 | Theories of friction (tribology) |
| 74M15 | Contact in solid mechanics |
| 74G30 | Uniqueness of solutions of equilibrium problems in solid mechanics |
| 74H25 | Uniqueness of solutions of dynamical problems in solid mechanics |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 35J85 | Unilateral problems; variational inequalities (elliptic type) (MSC2000) |
Keywords:
dry friction; boundary value problems; coupled system of partial differential equations; variational inequalities; existence; anisotropic friction law; quasistatic problem; linear elastic body; unilateral contact; rigid support; Coulomb’s friction law; power law normal compliance; incremental problem; rate problem; path dependenceReferences:
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