Quasistatic bilateral contact problem with time delay for viscoelastic materials

2016 ◽  
Vol 21 (9) ◽  
pp. 1068-1081
Author(s):  
Justyna Ogorzały
Keyword(s):  
Time Delay ◽  
Contact Problem ◽  
Viscoelastic Materials ◽  
Bilateral Contact

scholarly journals An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

2013 ◽  
Vol 23 (2) ◽  
pp. 263-276 ◽  
Author(s):  
Mikaël Barboteu ◽  
Krzysztof Bartosz ◽  
Piotr Kalita
Keyword(s):  
Contact Problem ◽  
Frictional Contact ◽  
Numerical Approach ◽  
Bundle Method ◽  
Nonconvex Problem ◽  
Proximal Bundle Method ◽  
Loss Of Contact ◽  
The Galerkin Method ◽  
Bilateral Contact ◽  
Numerical Approaches

We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.

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.

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