Analysis of a quasistatic viscoelastic problem with friction and damage.

*(English)*Zbl 0962.74044Summary: We consider a quasistatic frictional contact between a viscoelastic body and a reactive foundation. The material constitutive relation is nonlinear and viscoelastic. The contact is described by a general damped response condition, and by a modified Coulomb law of dry friction. We derive a variational formulation for the problem, and prove the existence of unique weak solution. We also propose a dual formulation of the problem, and establish the equivalence between two formulations. Then, we add the material damage which results from tension or compression as a dependent variable, and obtain the existence and uniqueness of weak solution for the problem with damage. Finally, we derive a dual formulation and establish its equivalence to the original problem.

##### MSC:

74M15 | Contact in solid mechanics |

74M10 | Friction in solid mechanics |

74D10 | Nonlinear constitutive equations for materials with memory |

74G20 | Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010) |

74G30 | Uniqueness of solutions of equilibrium problems in solid mechanics |

74R20 | Anelastic fracture and damage |