scholarly journals A quasistatic contact problem with adhesion and friction for viscoelastic materials

2010 ◽  
Vol 37 (1) ◽  
pp. 39-52
Author(s):  
Arezki Touzaline
Keyword(s):  
Contact Problem ◽  
Viscoelastic Materials

A quasistatic frictional contact problem for viscoelastic materials with long memory

2020 ◽  
Vol 27 (2) ◽  
pp. 249-264
Author(s):  
Abderrezak Kasri ◽  
Arezki Touzaline
Keyword(s):  
Contact Problem ◽  
Coefficient Of Friction ◽  
Frictional Contact ◽  
Time Discretization ◽  
Contact Boundary ◽  
Long Term Memory ◽  
Viscoelastic Materials ◽  
Existence Of A Solution ◽  
Frictional Contact Problem ◽  
The Coefficient Of Friction

AbstractThe aim of this paper is to study a quasistatic frictional contact problem for viscoelastic materials with long-term memory. The contact boundary conditions are governed by Tresca’s law, involving a slip dependent coefficient of friction. We focus our attention on the weak solvability of the problem within the framework of variational inequalities. The existence of a solution is obtained under a smallness assumption on a normal stress prescribed on the contact surface and on the coefficient of friction. The proof is based on a time discretization method, compactness and lower semicontinuity arguments.

An Incremental Adaptive Procedure for Viscoelastic Contact Problems

2006 ◽  
Vol 129 (2) ◽  
pp. 305-313 ◽  
Author(s):  
Fatin F. Mahmoud ◽  
Ahmed G. El-Shafei ◽  
Mohamed A. Attia
Keyword(s):  
Contact Problem ◽  
Contact Problems ◽  
Vital Role ◽  
Time Dependent ◽  
Viscoelastic Materials ◽  
Adaptive Procedure ◽  
Linear Behavior ◽  
Material Contact ◽  
Proposed Model ◽  
Deformable Bodies

Contact pressure distribution throughout the contact interface has a vital role on the tribological aspects of the contact systems. Generally, contact of deformable bodies is a nonlinear problem. Viscoelastic materials have a time-dependent response, since both viscous and elastic characteristics depend on time. Such types of materials have the capability of storing and dissipating energy. When at least one of the contacting bodies is made of a viscoelastic material, contact problems become more difficult, and a nonlinear time-dependent contact problem is obtained. The objective of this paper is to develop an incremental adaptive computational model capable of handling quasistatic viscoelastic frictionless contact problems. The Wiechert model, as an effective model capable of describing both creep and relaxation phenomena, is adopted to simulate the linear behavior of viscoelastic materials. The resulting constitutive integral equations are linearized and, therefore, complications that arise during the direct integration of these equations, specially with contact problems, are avoided. In addition, the incremental convex programming method is adopted and modified to accommodate the contact problem of viscoelastic bodies. The Lagrange multiplier method is adopted to enforce the contact constraints. Two different contact problems are presented to demonstrate the efficient applicability of the proposed model.

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