Existence and Uniqueness for Quasistatic Contact Problems with Friction

2002 ◽  
pp. 245-260
Author(s):  
Lars-Erik Andersson ◽  
Anders Klarbring
Keyword(s):  
Existence And Uniqueness ◽  
Contact Problems

A traction contact problem governed by hemivariational inequalities for a mixed formulation of Stokes equation

2016 ◽  
Vol 22 (3) ◽  
pp. 420-433 ◽  
Author(s):  
T Sluzalec
Keyword(s):  
Weak Solution ◽  
Velocity Field ◽  
Contact Problem ◽  
Stokes Equation ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Contact Problems ◽  
Mixed Formulation ◽  
Hemivariational Inequalities ◽  
The Stokes Equation

In this paper the traction contact problems for Stokes equation are discussed and the Stokes equation is considered in a mixed formulation. We prove the existence and uniqueness of the weak solution for a mixed formulation of Stokes equation with traction contact. The traction contact is described by subdifferential boundary conditions. For this problem we present a variational formulation in a form of a hemivariational inequality for the velocity field.

scholarly journals A CLASS OF QUASISTATIC CONTACT PROBLEMS FOR VISCOELASTIC MATERIALS WITH NONLOCAL COULOMB FRICTION AND TIME-DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 491-508 ◽  
Author(s):  
Si-sheng Yao ◽  
Nan-jing Huang
Keyword(s):  
Mathematical Model ◽  
Variational Inequality ◽  
Time Delay ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Contact Problems ◽  
Existence And Uniqueness Theorem ◽  
Differential Variational Inequality

In this paper, a mathematical model which describes the explicit time dependent quasistatic frictional contact problems is introduced and studied. The material behavior is described with a nonlinear viscoelastic constitutive law with time-delay and the frictional contact is modeled with nonlocal Coulomb boundary conditions. A variational formulation of the mathematical model is given, which is called a quasistatic integro-differential variational inequality. Using the Banach's fixed point theorem, an existence and uniqueness theorem of the solution for the quasistatic integro-differential variational inequality is proved under some suitable assumptions. As an application, an existence and uniqueness theorem of the solution for the dual variational formulation is also given.

scholarly journals Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Stanisław Migórski
Keyword(s):  
Mathematical Modeling ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Contact Problems ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
Uniqueness Of Solutions ◽  
Viscoelastic Contact

AbstractWe survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas leading to inequality problems with multivalued and nonmonotone boundary conditions encountered in mechanics.

Subdifferential inclusions for stress formulations of unilateral contact problems

2017 ◽  
Vol 23 (3) ◽  
pp. 392-410
Author(s):  
Mircea Sofonea ◽  
Krzysztof Bartosz
Keyword(s):  
Existence And Uniqueness ◽  
Deformable Body ◽  
Contact Problems ◽  
Unilateral Contact ◽  
Constitutive Law ◽  
Memory Term ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Uniqueness Of The Solution ◽  
Subdifferential Operators

We consider two classes of inclusions involving subdifferential operators, both in the sense of Clarke and in the sense of convex analysis. An inclusion that belongs to the first class is stationary while an inclusion that belongs to the second class is history-dependent. For each class, we prove existence and uniqueness of the solution. The proofs are based on arguments of pseudomonotonicity and fixed points in reflexive Banach spaces. Then we consider two mathematical models that describe the frictionless unilateral contact of a deformable body with a foundation. The constitutive law of the material is expressed in terms of a subdifferential of a nonconvex potential function and, in the second model, involves a memory term. For each model, we list assumptions on the data and derive a variational formulation, expressed in terms of a multivalued variational inequality for the stress tensor. Then we use our abstract existence and uniqueness results on the subdifferential inclusions and prove the unique weak solvability of each contact model. We end this paper with some examples of one-dimensional constitutive laws for which our results can be applied.

EXISTENCE AND UNIQUENESS OF SOLUTIONS OF THE DISCRETIZED CONTACT ELASTO-PLASTIC PROBLEM WITH ISOTROPIC HARDENING

2000 ◽  
Vol 10 (08) ◽  
pp. 1151-1179 ◽  
Author(s):  
EDUARD ROHAN
Keyword(s):  
Variational Inequalities ◽  
Fundamental Theorem ◽  
Existence And Uniqueness ◽  
Contact Problems ◽  
Isotropic Hardening ◽  
Plastic Strains ◽  
Uniqueness Of Solutions ◽  
Operator Equations

A class of quasistatic contact problems for elasto-plastic bodies with isotropic hardening is considered. The problems involve displacements, plastic strains and plastic multipliers. In the framework of multi-valued operator equations, the existence and uniqueness assertions for discretized reduced subproblems are proved using a fundamental theorem on variational inequalities.

Sign in / Sign up

Export Citation Format

Share Document