# zbMATH — the first resource for mathematics

Computational contact mechanics. 2nd ed. (English) Zbl 1104.74002
Berlin: Springer (ISBN 3-540-32608-1/hbk). xii, 518 p. (2006).
The book contains fourteen chapters and three appendices. In Chapter 1 “Introduction”, several contact problems and simple discretizations present the basic ideas and difficulties of contact mechanics, including coupled and impact problems. The second Chapter “Introduction to contact mechanics and weak forms” discusses the underlying theoretical background for finite deformation solid mechanics, including kinematics, weak forms, linearizations and simple hyperelastic constitutive equations. The third Chapter “Continuum solid mechanics and weak forms” discusses contact kinematics from the point of view of continuum mechanics. Chapter 4 “Contact kinematics” and Chapter 5 “Constitutive equations for contact interfaces” deal with the study of physical behaviour of contact interfaces for different material pairings, as well as with basic formulations for lubrication, adhesion and wear. Chapter 6 “Contact boundary value problem and weak form” deals with boundary value problems for frictionless and frictional contact, contains also different methods on how the contact constraints can be incorporated in the weak forms needed for finite element analysis. The discretization of solids in contact by finite element method is peformed in Chapter 7 “Discretization of the continuum”. The discretization of the contact interfaces is addressed in Chapter 8 “Discretization, small deformation contact” and in Chapter 9 “Discretization, large deformation contact” for linear and nonlinear geometry, respectively. Here interpolation functions and matrix formulations are given for two- and three-dimensional applications. Furthermore, new techniques such as mortar or Nitsche interpolations are discussed. Solution methods for contact problems are contained in Chapter 10 “Solution algorithms”. Here different methods of algorithmic treatment are considered for the solution of contact boundary value problems which were defined in the weak sense in Chapter 5. In Chapter 11 “Thermo-mechanical contact” the author treats the coupled thermo-mechanical problems of contact. This chapter is concerned with heat transfer at the contact interface, which depends upon the mechanical response. The contact of beam elements is of interest in the micro-mechanical modelling of woven fabrics. The formulation of kinematic contact conditions is different in this case, and hence has been derived in Chapter 12 “Contact beam”. Stability problems which include contact restrictions are discussed in Chapter 13 “Computation of critical points with contact constraints”. Adaptive methods for contact problems which are necessary to control the errors inherited in the finite element method are described in Chapter 14“Adaptive finite element methods for contact problems”. The objective of this chapter is to obtain a mesh which is optimal in the sense that the computational costs involved are minimal under the constraint that the error in the finite element solution is below a certain limit.
The first ed. was published in 2002 by Wiley (New York).

##### MSC:
 74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids 74M15 Contact in solid mechanics 74M10 Friction in solid mechanics 74S05 Finite element methods applied to problems in solid mechanics 74F05 Thermal effects in solid mechanics
PRONTO3D; AceGen
Full Text: