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A class of contact and friction dynamic problems in thermoelasticity and in thermoviscoelasticity. (English) Zbl 0899.73473
Summary: We consider a class of dynamical contact problems with friction in the framework of thermoelasticity and thermoviscoelasticity theories. The results are valid for both elastic and viscoelastic materials (with short and long memory terms), for contact conditions, of the power law type, both on the normal and on the tangential stress components, including also unilateral contact conditions on the temperature or heat flux. Some existence and nonexistence; unicity and nonunicity results are presented, as a function of the relationship between the elasticity, viscous, thermal and contact coefficients. This work extends previous results of Duvaut and Lions and of Martins and Oden for the elastodynamics case. We use a penalty method in order to take into account the variational inequality equations and a regularization method for the approximation of the friction functional.
74A55Theories of friction (tribology)
74M15Contact (solid mechanics)
74D05Linear constitutive equations (materials with memory)
74D10Nonlinear constitutive equations (materials with memory)
80A20Heat and mass transfer, heat flow