Viscoelastic Problems with Long Memory

Authors: Mircea Sofonea Andaluzia Matei

Publish Date: 2009

Volume: , Issue: , Pages: 1-14

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Abstract

For the problems in this chapter we assume that the behavior of the materials is described by a viscoelastic constitutive law with long memory We consider both static and quasistatic antiplane problems in which the friction conditions are either the Tresca law or its regularization For each model we derive a variational formulation that is in the form of an elliptic or evolutionary variational inequality with a Volterra integral term for the displacement eld Then by using the abstract results in Chapter 6 we derive existence uniqueness and convergence results for the weak solutions of the corresponding antiplane frictional contact problems In particular we study the behavior of the solutions as the relaxation coecient converges to zero and prove that they converge to the solution of the corresponding purely elastic problems Again everywhere in this chapter we use the space V page 152 endowed with its inner product ··V and the associated norm cdot v and we denote by 0 T the time interval of interestT = 0 Also everywhere in this chapter the use of the abstract results presented in Part II of this manuscript is made in the case X = V ··X = ··V without explicit specication

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