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### A Dynamic Frictionless Contact Problem with Adhesion and Damage

Bulletin of the Polish Academy of Sciences. Mathematics

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...

### A dynamic problem with adhesion and damage in electro-viscoelasticity with long-term memory.

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

### A frictional contact problem for an electro-viscoelastic body.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### A frictional contact problem with adhesion for viscoelastic materials with long memory

Applications of Mathematics

We consider a quasistatic contact problem between a viscoelastic material with long-term memory and a foundation. The contact is modelled with a normal compliance condition, a version of Coulomb's law of dry friction and a bonding field which describes the adhesion effect. We derive a variational formulation of the mechanical problem and, under a smallness assumption, we establish an existence theorem of a weak solution including a regularity result. The proof is based on the time-discretization...

### A general asymptotic dynamic model for Lipschitzian elastic curved rods.

Journal of Applied Mathematics

### A quasistatic contact problem with adhesion and friction for viscoelastic materials

Applicationes Mathematicae

We consider a mathematical model which describes the contact between a deformable body and a foundation. The contact is frictional and is modelled by a version of normal compliance condition and the associated Coulomb's law of dry friction in which adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behaviour is modelled by a nonlinear viscoelastic constitutive law. We derive a variational formulation...

### A quasistatic unilateral and frictional contact problem with adhesion for elastic materials

Applicationes Mathematicae

We consider a quasistatic contact problem between a linear elastic body and a foundation. The contact is modelled with the Signorini condition and the associated non-local Coulomb friction law in which the adhesion of the contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation of the mechanical problem and prove existence of a weak solution if the friction coefficient is sufficiently small....

### A study of a unilateral and adhesive contact problem with normal compliance

Applicationes Mathematicae

The aim of this paper is to study a quasistatic unilateral contact problem between an elastic body and a foundation. The constitutive law is nonlinear and the contact is modelled with a normal compliance condition associated to a unilateral constraint and Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation...

### A system of semilinear evolution equations with homogeneous boundary conditions for thin plates coupled with membranes.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### A transmission problem for beams on nonlinear supports.

Boundary Value Problems [electronic only]

### A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy

Annales de l'I.H.P. Analyse non linéaire

### A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies

ESAIM: Control, Optimisation and Calculus of Variations

Rate-independent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obtained in terms of compatible systems of Young measures. We also show as this result can be equivalently reformulated with probabilistic language and leads to the description of the quasistatic evolution in terms...

### A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies

ESAIM: Control, Optimisation and Calculus of Variations

Rate-independent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obtained in terms of compatible systems of Young measures. We also show as this result can be equivalently reformulated with probabilistic language and leads to the description of the quasistatic evolution in terms...

### An elastic membrane with an attached non-linear thermoelastic rod

International Journal of Applied Mathematics and Computer Science

We study a thermo-mechanical system consisting of an elastic membrane to which a shape-memory rod is glued. The slow movements of the membrane are controlled by the motions of the attached rods. A quasi-static model is used. We include the elastic feedback of the membrane on the rods. This results in investigating an elliptic boundary value problem in a domain Ω ⊂ R^2 with a cut, coupled with non-linear equations for the vertical motions of the rod and the temperature on the rod. We prove the existence...

### Analysis of a contact adhesive problem with normal compliance and nonlocal friction

Annales Polonici Mathematici

The paper deals with the problem of a quasistatic frictional contact between a nonlinear elastic body and a deformable foundation. The contact is modelled by a normal compliance condition in such a way that the penetration is restricted with a unilateral constraint and associated to the nonlocal friction law with adhesion. The evolution of the bonding field is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove an existence...

### Analysis of electroelastic frictionless contact problems with adhesion.

Journal of Applied Mathematics

### Analysis of electro-viscoelastic antiplane contact problem with total slip rate dependent friction.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Analysis of two dynamic frictionless contact problems for elastic-viscoplastic materials.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Antiplane frictional contact of electro-viscoelastic cylinders.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Asymptotic analysis for vanishing acceleration in a thermoviscoelastic system.

Abstract and Applied Analysis

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