A Dynamic Frictionless Contact Problem with Adhesion and Damage

Abstract

Summary. We consider a dynamic frictionless contact problem for a viscoelastic material with damage. The contact is modeled with normal compliance condition. The adhesion of the contact surfaces is considered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We establish a variational formulation for the problem and prove the existence and uniqueness of the solution. The proofs are based on the theory of evolution equations with monotone operators, a classical existence and uniqueness result for parabolic inequalities, and fixed point arguments.

A frictional contact problem with normal damped response for elastic-visco-plastic materials

“…(14) represents the equation of motion where ρ denotes the material mass density, (15) and (16) are the displacement and traction boundary conditions, respectively. Condition (17) represents the normal damped response condition and a local friction law described above. (18) represents a homogeneous Neumann boundary condition where ∂α ∂ν represents the normal derivative of α.…”

“…Condition (17) represents the normal damped response condition and a local friction law described above. (18) represents a homogeneous Neumann boundary condition where ∂α ∂ν represents the normal derivative of α. In (19), we consider the initial conditions where u 0 is the initial displacement, v 0 the initial velocity and α 0 is the initial damage.…”

“…[6,11,12,13,15,19,20] and the recent references 1, 13 . Contact problem for viscoelastic materials of the form (3) are considered in 10,16,17,20 . Contact problems for elastic-visco-plastic materials of the form (2) where the damage is caused by plastic déformations and whose evolution is described by a differential inclusion of parabolic type are studied in 2, 18, 20 .…”

A Dynamic Frictionless Elastic-Viscoplastic Problem with Normal Damped Response and Damage

“…[6,11,12,15,19,20] and the recent references [1,13]. Contact problems for elastic-viscoplastic materials of the form (1.2) are studied in [2,5,18,20]. The damage subject is extremely important in design engineering, since it directly affects the useful life of the designed structure or component.…”

“…When β = 1 there is no damage in the material, when β = 0 the material is completely damaged, when 0 < β < 1 there is partial damage and the system has a reduced load carrying capacity. Contact problems with damage have been investigated in [10,16,17,18,20]. In this paper the inclusion used for the evolution of the damage field is…”