A regularization method for a viscoelastic contact problem

2016 ◽  
Vol 23 (2) ◽  
pp. 181-194
Author(s):  
Flavius Pătrulescu
Keyword(s):  
Mathematical Model ◽  
Contact Problem ◽  
Variational Inequalities ◽  
Long Memory ◽  
Regularization Method ◽  
Viscoelastic Body ◽  
Constitutive Law ◽  
Normal Compliance ◽  
Viscoelastic Contact

We consider a mathematical model which describes the quasistatic contact between a viscoelastic body and a deformable obstacle, the so-called foundation. The material’s behaviour is modelled with a viscoelastic constitutive law with long memory. The contact is frictionless and is defined using a multivalued normal compliance condition. We present a regularization method in the study of a class of variational inequalities involving history-dependent operators. Finally, we apply the abstract results to analyse the contact problem.

scholarly journals A VISCOELASTIC CONTACT PROBLEM WITH ADHESION AND SURFACE MEMORY EFFECTS

2014 ◽  
Vol 19 (5) ◽  
pp. 607-626 ◽  
Author(s):  
Mircea Sofonea ◽  
Flavius Patrulescu
Keyword(s):  
Long Memory ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Viscoelastic Body ◽  
Uniqueness Result ◽  
Unilateral Constraint ◽  
Memory Effects ◽  
Constitutive Law ◽  
Classical Formulation ◽  
Viscoelastic Contact

We consider a mathematical model which describes the quasistatic contact between a viscoelastic body and an obstacle, the so-called foundation. The material's behavior is modelled with a constitutive law with long memory. The contact is with normal compliance, unilateral constraint, memory effects and adhesion. We present the classical formulation of the problem, then we derive its variational formulation and prove an existence and uniqueness result. The proof is based on arguments of variational inequalities and fixed point.

scholarly journals Numerical Analysis of a Sliding frictional contact problem with Normal Compliance and Unilateral Contact

2020 ◽  
Author(s):  
Yahyeh Souleiman ◽  
Mikael Barboteu
Keyword(s):  
Numerical Analysis ◽  
Contact Problem ◽  
Frictional Contact ◽  
Nonlinear Partial Differential Equations ◽  
Viscoelastic Body ◽  
Sliding Contact ◽  
Memory Term ◽  
Optimal Order ◽  
Normal Compliance ◽  
Order Error

Abstract This paper represents a continuation of [15] and [18]. Here, we consider the numerical analysis of a non trivial frictional contact problen in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint, and is associated to a sliding version of Coulomb's law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.

VISCOELASTIC ADHESION OF A SPHERICAL TIP INDENTING A FLAT RIGID SURFACE USING LENNARD-JONES INTERACTION

2015 ◽  
Vol 76 (10) ◽  
Author(s):  
A.K.X. Leong ◽  
W.W.F. Chong
Keyword(s):  
Mathematical Model ◽  
Contact Problem ◽  
Physical Properties ◽  
Contact Problems ◽  
Surface Forces ◽  
Elastic Contact ◽  
Rigid Surface ◽  
Lennard Jones ◽  
Viscoelastic Contact

Solid and elastic contact problems have been thoroughly investigated before. The most recent efforts incorporate the use of the Lennard-Jones (LJ) potential to describe the inter-surface forces that are present and substantial in micro-sized contact problems. But little work has been done on viscoelastic contact problems. Hence, there is a need to investigate the behaviour of a viscoelastic contact under the LJ interaction. This paper aims to investigate the deformation of an axisymmetric viscoelastic tip that is either pushed onto or pulled from a flat rigid surface. From existing elastic models, a mathematical model was developed to describe the contact problem in a viscoelastic context. This newly developed was solved via numerical means. The result is a model that readily accepts measureable physical properties and gives out the deformation of a viscoelastic tip.

On quasi-static contact problem with generalized Coulomb friction, normal compliance and damage

2015 ◽  
Vol 27 (4) ◽  
pp. 625-646 ◽  
Author(s):  
LESZEK GASIŃSKI ◽  
PIOTR KALITA
Keyword(s):  
Contact Problem ◽  
Coulomb Friction ◽  
Fixed Point Theory ◽  
Viscoelastic Body ◽  
The Body ◽  
Damage Effect ◽  
Contact Boundary ◽  
Normal Compliance ◽  
Friction Law ◽  
Static Contact

In this paper, we study a quasi-static frictional contact problem for a viscoelastic body with damage effect inside the body as well as normal compliance condition and multi-valued friction law on the contact boundary. The considered friction law generalizes Coulomb friction condition into multi-valued setting. The variational–hemi-variational formulation of the problem is derived and arguments of fixed point theory and surjectivity results for pseudo-monotone operators are applied, in order to prove the existence and uniqueness of solution.

scholarly journals A Quasistatic Contact Problem for Viscoelastic Materials with Slip-Dependent Friction and Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
Si-sheng Yao ◽  
Nan-jing Huang
Keyword(s):  
Mathematical Model ◽  
Variational Inequality ◽  
Time Delay ◽  
Contact Problem ◽  
Deformable Body ◽  
Constitutive Law ◽  
Time Dependent ◽  
Delay Term ◽  
Inequality System ◽  
Differential Variational Inequality

A mathematical model which describes an explicit time-dependent quasistatic frictional contact problem between a deformable body and a foundation is introduced and studied, in which the contact is bilateral, the friction is modeled with Tresca’s friction law with the friction bound depending on the total slip, and the behavior of the material is described with a viscoelastic constitutive law with time delay. The variational formulation of the mathematical model is given as a quasistatic integro-differential variational inequality system. Based on arguments of the time-dependent variational inequality and Banach's fixed point theorem, an existence and uniqueness of the solution for the quasistatic integro-differential variational inequality system is proved under some suitable conditions. Furthermore, the behavior of the solution with respect to perturbations of time-delay term is considered and a convergence result is also given.

A dynamic viscoelastic contact problem with normal compliance and damage

2005 ◽  
Vol 42 (1) ◽  
pp. 1-24 ◽  
Author(s):  
M. Campo ◽  
J.R. Fernández ◽  
W. Han ◽  
M. Sofonea
Keyword(s):  
Contact Problem ◽  
Normal Compliance ◽  
Viscoelastic Contact
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