A convergence result in elastic-viscoplastic contact problems with damage

Dynamic nonsmooth frictional contact problems with damage in thermoviscoelasticity

“…where ∂I [0,1] denotes the convex subdifferential of the indicator function I [0,1] of an interval [0, 1] (cf. Campo et al [6], Chau and Fernandez [9], Shillor et al [2] and Sofonea et al [3] for details). For examples of the damage function which satisfies the hypothesis H ( φ ), we refer to Section 12 of Shillor et al [2].…”

“…The corresponding quasistatic contact problems with normal compliance and damage have been considered in several papers, e.g. Han et al [8] for problems with Coulomb’s law of dry friction, Chau et al [9, 10] and Campo et al [11, 12] for frictionless models. Results on the evolution of damage in elastic–viscoplastic quasistatic problems without contact can be found in Kuttler [13].…”

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

“…In [10,11,20] (see the monograph [32] for details), this is replaced by a parabolic subdifferential inclusion because a constraint condition must be imposed. In this paper, this condition is obtained from the assumptions required to the damage source function φ.…”

“…Mathematical problems including damage have been studied recently for elastic materials [4,5,9], elastic-viscoplastic materials [7,10,11] or viscoelastic materials [6,20]. Moreover, one-dimensional problems have been also considered (see, e.g., [1]).…”

Numerical Analysis of a Unilateral Problem in Planar Thermoelasticity

“…Quasi-static and dynamic problems with Barber's heat exchange condition were studied by Xu [19] and Bien [3], respectively. The papers [2], [5], and [6] provide error analysis for some contact problems in elasticity. A static problem in thermoelasticity with many bodies in contact is numerically approximated by the finite element method in [13].…”