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**Contact mechanics.**
*(English)*
Zbl 0599.73108

Cambridge etc.: Cambridge University Press. XI, 452 p. £45.00; $ 89.50 (1985).

According to the author ”the aim of the present book is... to provide an introduction to most aspects of the mechanics of contact between non- conforming surfaces” (surfaces are non-conforming if bodies in contact have dissimilar profiles). In reviewer’s opinion this aim has been achieved due to well organized and simple presentation of the topics considered. The book comprises 13 chapters and 5 appendices.

Typical for non-conforming contact are line and concentrated loadings. The contact problems for a linear elastic half-space subject to various kinds of such loadings are presented in two subsequent chapters.

As is known, contact mechanics was founded by Hertz in 1882. For the Hertz theory to be valid, the following restrictions have to be imposed: linear elastic half-space theory, frictionless contact and parabolic profiles. Non-Hertzian contact of elastic solids is studied in a separate chapter, where such important aspects of contact as influence of friction and adhesion are also investigated. Variational methods are mentioned, yet the discussion does not reflect at all the progress attained in this domain of contact problems (see the additional references given below).

For a normal contact of an indenter with rigid-plastic bodies the theory of slip-lines constitute now the classical branch of the theory of plasticity. The book is restricted to metal plasticity; soils are not discussed. The influence of elasticity on the process of contact as well as the unloading of a plastic indentation are carefully discussed. Viscoelastic contact is studied by examples mainly of materials which display delayed elasticity and Maxwell bodies. Nonlinear elasticity and creep are restricted to materials obeying the power constitutive law.

In Chapter 7 various situations of practically important interaction between normal and tangential loadings are investigated for linearly elastic and rigid-perfectly-plastic bodies. Torsion of elastic spheres is also studied. Discussion of oscillating force leads naturally to the surface damage known as ”fretting”. The mechanics of the rolling contact of elastic, viscoelastic and plastic bodies is carefully studied in Chapters 8 and 9. A technologically important class of problems constitutes the contact of elastic or plastic strips compressed by rollers. A new class of contact problems arises when lubrication is taken into account. In the case of dynamic contact the most important effect is the generation of surface waves (Chapter 11). This chapter also deals with elastic and inelastic impact. Chapter 12 introduces basic concepts related to contact problems when temperature effects have to be taken into account. In general contacting surfaces are not smooth due to the presence of asperities. The last chapter presents various aspects of discontinuous contact (rough surfaces).

The list of references is quite impressive yet I would like to add at least the following publications on variational methods in contact mechanics: G. Del Piero and F. Maceri (eds.), Unilateral problems in structural analysis (1985; Zbl 0581.00018); G. Duvaut, Finite elasticity, Proc. IUTAM Symp. Bethlehem/PA. 1980, 151-166 (1982; Zbl 0516.73122) and P. D. Panagiotopoulos, Inequality problems in mechanics and applications (1985; Zbl 0579.73014).

A forthcoming comprehensive paper by the reviewer [Variational methods in contact problems of mechanics, Adv. in Mechanics (1987, in Russian)] overviews all important aspects of variational methods used to solve elastic and inelastic contact problems. The results presented by K. L. Johnson are obtained under assumptions which are in large part dispensable if variational methods are employed. Contact problems are usually of ”free boundary problems” type. Therefore variational methods like variational and quasi-variational inequalities are very appropriate for both qualitative and numerical analysis.

The book, written by the author who largely contributed to contact mechanics, will primarily appeal to mechanical engineers. However it should also be of interest to mathematically inclined researchers and particularly to those engaged in free boundary problems. The author succeeded in a clear and very nice presentation of both classical and non-classical problems of contact mechanics. Therefore I strongly recommend his book.

Typical for non-conforming contact are line and concentrated loadings. The contact problems for a linear elastic half-space subject to various kinds of such loadings are presented in two subsequent chapters.

As is known, contact mechanics was founded by Hertz in 1882. For the Hertz theory to be valid, the following restrictions have to be imposed: linear elastic half-space theory, frictionless contact and parabolic profiles. Non-Hertzian contact of elastic solids is studied in a separate chapter, where such important aspects of contact as influence of friction and adhesion are also investigated. Variational methods are mentioned, yet the discussion does not reflect at all the progress attained in this domain of contact problems (see the additional references given below).

For a normal contact of an indenter with rigid-plastic bodies the theory of slip-lines constitute now the classical branch of the theory of plasticity. The book is restricted to metal plasticity; soils are not discussed. The influence of elasticity on the process of contact as well as the unloading of a plastic indentation are carefully discussed. Viscoelastic contact is studied by examples mainly of materials which display delayed elasticity and Maxwell bodies. Nonlinear elasticity and creep are restricted to materials obeying the power constitutive law.

In Chapter 7 various situations of practically important interaction between normal and tangential loadings are investigated for linearly elastic and rigid-perfectly-plastic bodies. Torsion of elastic spheres is also studied. Discussion of oscillating force leads naturally to the surface damage known as ”fretting”. The mechanics of the rolling contact of elastic, viscoelastic and plastic bodies is carefully studied in Chapters 8 and 9. A technologically important class of problems constitutes the contact of elastic or plastic strips compressed by rollers. A new class of contact problems arises when lubrication is taken into account. In the case of dynamic contact the most important effect is the generation of surface waves (Chapter 11). This chapter also deals with elastic and inelastic impact. Chapter 12 introduces basic concepts related to contact problems when temperature effects have to be taken into account. In general contacting surfaces are not smooth due to the presence of asperities. The last chapter presents various aspects of discontinuous contact (rough surfaces).

The list of references is quite impressive yet I would like to add at least the following publications on variational methods in contact mechanics: G. Del Piero and F. Maceri (eds.), Unilateral problems in structural analysis (1985; Zbl 0581.00018); G. Duvaut, Finite elasticity, Proc. IUTAM Symp. Bethlehem/PA. 1980, 151-166 (1982; Zbl 0516.73122) and P. D. Panagiotopoulos, Inequality problems in mechanics and applications (1985; Zbl 0579.73014).

A forthcoming comprehensive paper by the reviewer [Variational methods in contact problems of mechanics, Adv. in Mechanics (1987, in Russian)] overviews all important aspects of variational methods used to solve elastic and inelastic contact problems. The results presented by K. L. Johnson are obtained under assumptions which are in large part dispensable if variational methods are employed. Contact problems are usually of ”free boundary problems” type. Therefore variational methods like variational and quasi-variational inequalities are very appropriate for both qualitative and numerical analysis.

The book, written by the author who largely contributed to contact mechanics, will primarily appeal to mechanical engineers. However it should also be of interest to mathematically inclined researchers and particularly to those engaged in free boundary problems. The author succeeded in a clear and very nice presentation of both classical and non-classical problems of contact mechanics. Therefore I strongly recommend his book.

Reviewer: J.J.Telega

### MSC:

74A55 | Theories of friction (tribology) |

74M15 | Contact in solid mechanics |

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |

74C99 | Plastic materials, materials of stress-rate and internal-variable type |

74B20 | Nonlinear elasticity |

35R35 | Free boundary problems for PDEs |