A quasistatic contact problem with slip‐dependent coefficient of friction

We consider a mathematical model which describes the bilateral quasistatic contact of a viscoelastic body with a rigid obstacle. The contact is modelled with a modified version of Coulomb's law of dry friction and. moreover, the coefficient of friction is assumed to depend either on the total slip or on the current slip. In the first case, the problem depends upon contact history. We present the classical formulations of the problems. the variational formulations and establish the existence and uniqueness of a weak solution to each of them. when the coefficient of friction is sufficiently small. The proofs are based on classical results for elliptic variational inequalities and fixed point arguments. We also study the dependence of the solutions on the perturbations of the friction coefficient and obtain a uniform convergence result.

[1]  M. Cocu,et al.  Existence of solutions of Signorini problems with friction , 1984 .

[2]  Meir Shillor,et al.  On the dynamic behaviour of a thermoviscoelastic body in frictional contact with a rigid obstacle , 1997, European Journal of Applied Mathematics.

[3]  M. Cocu,et al.  Formulation and approximation of quasistatic frictional contact , 1996 .

[4]  Meir Shillor,et al.  A dynamic thermoviscoelastic contact problem with friction and wear , 1997 .

[5]  Mircea Sofonea,et al.  Functional and numerical methods in viscoplasticity , 1993 .

[6]  J.-C. Paumier,et al.  On the contact problem with slip rate dependent friction in elastodynamics , 1994 .

[7]  P. Panagiotopoulos.  Inequality problems in mechanics and applications , 1985 .

[8]  Mircea Sofonea.  On a contact problem for elastic-viscoplastic bodies , 1997 .

[9]  J. T. Oden,et al.  Models and computational methods for dynamic friction phenomena , 1984 .

[10]  L. Andersson,et al.  A quasistatic frictional problem with normal compliance , 1991 .

[11]  L. Johansson,et al.  Derivation and analysis of a generalized standard model for contact, friction and wear , 1996 .

[12]  Niclas Strömberg.  Continuum Thermodynamics of Contact Friction and Wear , 1995 .

[13]  Meir Shillor,et al.  A Global Existence Result for the Quasistatic Frictional Contact Problem with Normal Compliance , 1991 .

[14]  Mircea Sofonea,et al.  Analysis of a quasistatic viscoplastic problem involving tresca friction law , 1997 .