Nonlinear Inclusions and Hemivariational Inequalities
Models and Analysis of Contact Problems
Page
%P
27 Result(s)
-
Article
History-Dependent Inequalities for Contact Problems with Locking Materials
We consider a class of history-dependent variational–hemivariational inequalities with constraints. Besides the unique solvability of the inequalities, we study the behavior of the solution with respect to the...
-
Article
Open AccessA Class of Variational-Hemivariational Inequalities in Reflexive Banach Spaces
We study a new class of elliptic variational-hemivariational inequalities in reflexive Banach spaces. An inequality in the class is governed by a nonlinear operator, a convex set of constraints and two nondiff...
-
Book
-
Chapter
Preliminaries
In this chapter we present preliminary material from functional analysis which will be used subsequently. The results are stated without proofs, since they are standard and can be found in many references. For...
-
Chapter
Elements of Nonlinear Analysis
In this chapter we present basic material on the set-valued map**s, nonsmooth analysis, subdifferential calculus, and operators of monotone type. For set-valued map**s we concentrate on measurability and c...
-
Chapter
Evolutionary Inclusions and Hemivariational Inequalities
In this chapter we study evolutionary inclusions of second order. These are multivalued relations which involve the second-order time derivative of the unknown. We start with a basic existence result for such ...
-
Chapter
Analysis of Static Contact Problems
In this chapter we illustrate the use of the abstract results obtained in Chap. 4, in the study of three representative static frictional contact problems for deformable bodies. In the first two problems we mo...
-
Chapter
Function Spaces
In this chapter we introduce function spaces that will be relevant to the subsequent developments in this monograph. The function spaces to be discussed include spaces of continuous and continuously differenti...
-
Chapter
Stationary Inclusions and Hemivariational Inequalities
In this chapter we study stationary operator inclusions, i.e., inclusions in which the derivatives of the unknown with respect to the time variable are not involved. We start with a basic existence result for ...
-
Chapter
Modeling of Contact Problems
In this chapter we deal with the mathematical modeling of the processes of contact between a deformable body and a foundation. We present the physical setting, the variables which determine the state of the sy...
-
Chapter
Analysis of Dynamic Contact Problems
In this chapter we apply the abstract results of Chap. 5 in the study of three dynamic frictional contact problems. In the first two problems we model the material’s behavior with a nonlinear viscoelastic cons...
-
Chapter
Modelling of Piezoelectric Contact Problems
We consider a mathematical model which describes the frictional contact between an electro-viscoelastic body and a conductive foundation. The process is dynamic and the contact is modelled with normal complian...
-
Book
-
Chapter
1 Introduction
Considerable progress has been achieved recently in modeling and mathematical analysis of various processes involved in contact between deformable bodies. Indeed, a general Mathematical Theory of Contact Mecha...
-
Chapter
5 A Detailed Representative Problem
In the previous three chapters various constitutive laws for the behaviour of the material and different contact conditions were described in some detail. In this chapter we take the next step and assemble, in...
-
Chapter
10 Slip or Temperature Dependent Frictional Contact
The frictional contact problems which have been described up to now contained a constant friction coefficient, although, as was described in Sect. 2.7, in many applications it depends on the slip speed, on the...
-
Chapter
7 Elastic Contact
Existence results for the problem of quasistatic contact between an elastic material and a reactive foundation were first obtained in [18] and [19]. In both papers the normal compliance contact condition was e...
-
Chapter
12 Contact with Damage
We describe new results dealing with contact problems for materials that may undergo internal damage, resulting from strains and stresses which lead to the opening and growth of microscopic cracks. The damage ...
-
Chapter
14 Conclusions, Remarks and Future Directions
This monograph shows clearly that the branch of the Mathematical Theory of Contact Mechanics which deals with quasistatic processes has made an impressive progress in the last decade. Indeed, from a handful of...
-
Chapter
4 Thermodynamic Derivation
In this chapter we present a short review of thermodynamic principles and potentials and describe their use in derivation of general thermomechanical conditions and equations, as applied to processes involved ...
