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Analysis of a quasistatic viscoelastic problem with friction and damage. (English) Zbl 0962.74044
Summary: 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.

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