Dynamic friction contact problems for general normal and friction laws

1997 ◽  
Vol 28 (3) ◽  
pp. 559-575 ◽  
Author(s):  
K.L. Kuttler
Keyword(s):  
Contact Problems ◽  
Dynamic Friction ◽  
Friction Contact ◽  
Friction Laws

Optimal control for antiplane frictional contact problems involving nonlinearly elastic materials of Hencky type

2017 ◽  
Vol 23 (3) ◽  
pp. 308-328 ◽  
Author(s):  
Andaluzia Matei ◽  
Sorin Micu ◽  
Constantin Niţǎ
Keyword(s):  
Optimal Control ◽  
Frictional Contact ◽  
Variational Equation ◽  
Optimal Solution ◽  
Contact Problems ◽  
Point Of View ◽  
Friction Laws ◽  
Convergence Results ◽  
Positive Exponent ◽  
Nonlinearly Elastic

We consider an antiplane contact problem modeling the friction between a nonlinearly elastic body of Hencky type and a rigid foundation. We discuss the well-posedness of the model by considering two friction laws. Firstly, Tresca’s law is used to describe the friction force and leads to a variational inequality. Alternatively, a regularizing power law with a positive exponent r is considered and gives, from the mathematical point of view, a variational equation. In both contexts, we address a boundary optimal control problem by minimizing, on a nonconvex set, a cost functional with two arguments. We show the existence of at least one optimal pair for each problem. Finally, we deliver some convergence results proving that the optimal solution of the regular problem tends, when r goes to zero, to an optimal solution of the first one.

Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problems in Elasticity

1983 ◽  
Vol 50 (1) ◽  
pp. 67-76 ◽  
Author(s):  
J. T. Oden ◽  
E. B. Pires
Keyword(s):  
Variational Principles ◽  
Nonlinear Problems ◽  
Contact Problems ◽  
Nonlinear Friction ◽  
Metallic Surfaces ◽  
Uniqueness Of Solutions ◽  
Friction Laws ◽  
Elastic Bodies ◽  
Mathematical Difficulties ◽  
And Variational Principles

The use of the classical Coulomb law of friction in the formulation of contact problems in elasticity leads to both physical and mathematical difficulties; the former arises from the fact that this law provides a poor model of frictional stresses at points on metallic surfaces in contact, and the latter is due to the fact that the existence of solutions of the governing equations can be proved only for very special situations. In the present paper, nonclassical friction laws are proposed in an attempt to overcome both of these difficulties. We consider a class of contact problems involving the equilibrium of linearly elastic bodies in contact on surfaces on which nonlocal and nonlinear friction laws are assumed to hold. The physics of friction between metallic bodies in contact is discussed and arguments in support of the theory are presented. Variational principles for boundary-value problems in elasticity in which such nonlinear nonlocal laws hold are then developed. A brief discussion of the questions of existence and uniqueness of solutions to the nonlocal and nonlinear problems is given.

The use of static reduction in the finite element solution of two-dimensional frictional contact problems

2013 ◽  
Vol 228 (9) ◽  
pp. 1474-1487 ◽  
Author(s):  
A Thaitirarot ◽  
RC Flicek ◽  
DA Hills ◽  
JR Barber
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Frictional Contact ◽  
Contact Problems ◽  
Computational Time ◽  
Friction Laws ◽  
Periodic Loading ◽  
Frictional System ◽  
Well Posed

In this paper, detailed instructions are given for performing static reduction on a finite element description of an elastic contact problem, thus reducing the dimensionality of the problem to the set of contact nodes alone. This significantly reduces the computational time for the solution to evolutionary contact problems and also gives the user greater control over the detailed implementation of the contact and friction laws. The reduced stiffness matrix is also an essential ingredient in the determination of the critical coefficient of friction for the problem to be well posed, and it facilitates the determination of the conditions under which a frictional system may shake down under periodic loading.

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