Viscoelastic Problems with Short Memory
In this chapter, we study quasistatic models for antiplane frictional problems involving viscoelastic materials with short memory. We model the friction with versions of Coulomb’s law, including Tresca’s law and its regularization, slip-dependent and total slip-dependent laws. For all the models, we prove that the displacement .eld satis.es an evolutionary variational inequality with viscosity. Then we apply the results in Chapter 4 to obtain existence, uniqueness, regularity, and convergence results. In this chapter, we use again the space V (page 152), together with its inner product (·,·)V and the associated norm \(||\cdot||\ v\). Moreover, [0, T] represents the time interval of interest, T > 0. Finally, we note that everywhere in this chapter, the use of the abstract results presented in Part II of this book is made in the case X = V , (·,·)X = (·,·)V , without explicit specication.
KeywordsBilinear Form Contact Problem Slip Rate Unique Weak Solution Frictional Contact Problem
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