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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.

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
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