A quasistatic contact problem with normal compliance and damage involving viscoelastic materials with long memory

A Class of Quasistatic Contact Problems for Viscoelastic Materials With Nonlocal Coulomb Friction and Time-Delay

“…Example 2. Contact problems involving viscoelastic materials with long memory are a class of important problems, which have been studied by many authors, such as in [4,10]. For more details on the long memory models, we refer to [13,20].…”

A quasistatic frictional contact problem with damage involving viscoelastic materials with short memory

“…More recently, existence and uniqueness results for quasistatic bilateral contact problems with damage, and the simplified Coulomb law of dry friction involving viscoplastic materials have been obtained by Campo et al [8]. The existence and uniqueness of a weak solution to the quasistatic frictionless contact problem with damage of a viscoelastic body with long memory can be found in Campo et al [9]. Quasistatic contact problems with damage for viscoelastic material with long memory and the subdifferential contact and friction conditions were studied in Li and Liu [12] in the framework of hemivariational inequalities.…”

“…Quasistatic contact problems with normal compliance and damage have been considered in several papers. Such problems with Coulomb's law of dry friction were studied in Han et al [5] and frictionless quasistatic models were analysed in Chau and Ferna´ndez [6], Chau et al [7], and Campo et al [8,9]. Results on the evolution of damage in elastic-viscoplastic and elastic materials in quasistatic problems without contact can be found in Kuttler [10], and Kuttler and Shillor [11], respectively.…”

Bilateral Contact Problem with Adhesion between Two Bodies for Viscoelastic with Long-term Memory and Damage

“…Here A is a given nonlinear operator, F is the relaxation operator, and G represents the elasticity operator. In (1) and everywhere in this paper the dot above a variable represents derivative with respect to the time variable t. It follows from (1) that at each time moment, the stress tensor σ (t) is split into two parts: σ (t) = σ V (t) + σ R (t), where σ V (t) = A ε(u (t)) represents the purely viscous part of the stress, and σ R (t) satisfies the rate-type elastic relation σ R (t) = G ε(u (t)) + t 0 F t − s, ε(u (s)), α (s) ds. (2) Various results, example and mechanical interpretations in the study of elastic materials of the form (2) can be found in [1,17] and references therein.…”