5R45. Fundamentals of Surface Mechanics with Applications, Second Edition. Mechanical Engineering Series. - FF Ling (Manuf Syst Center, Univ of Texas, Austin TX 78712), WM Lai (Dept of Mech Eng, Columbia Univ, New York NY 10027), DA Lucca (Sch of Mech and Aerospace Eng, Oklahoma State Univ, Stillwater OK 74078). Springer-Verlag, New York. 2002. 392 pp. ISBN 0-387-95423-6. $69.95.
Reviewed by P Puri (Dept of Math, Univ of New Orleans, 2000 Lakeshore Dr, New Orleans LA 70148).
This is a very well written book. The reader is assumed to be familiar with introductory continuum mechanics. Adequate references are given for the elementary continuum mechanics. This book explores the topic of surface mechanics using classical continuum mechanics throughout. The authors have successfully accomplished their stated purpose of setting down concrete examples dealing with surface mechanics and of providing analytical tools relevant to quantitative study of surface mechanics. The book can be used as a reference for understanding fundamental problems in surface mechanics by researchers and can also be used as textbook on this subject. While the book covers a wide range of topics, no mention of surface waves has been made. The organization of the material is as follows:
Chapter 1 is concerned with the basic equations of balance of momentum and energy, a discussion of entropy, constitutive equations, and energy balance for an elastic solid. Then there is a section on constitutive relations for heat conduction. Fick’s and Darcy’s laws are given in Section 6. Sections 7–11 contain constitutive relations for linearly viscous fluids, perfectly plastic bodies, viscoelastic bodies, Maxwellian dielectric, and classical electromagnetic theory, respectively. This chapter can be used as quick reference for constitutive equations for a variety of combined fields.
The first section in each of the remaining chapters introduces the main subject of the chapter. There are, in all, 24 main sections in Chapter 2. Sections 2–16, 18, and 22 give solutions to some typical problems of heat conduction. Section 17 is on the finite Fourier transform, 19 on Legendre polynomials, 20 on Legendre series, 21 on the Legendre transform, 23 on the Fourier cosine transform, and Section 24 contains a discussion on the effects of temperature dependent thermal conductivity and specific heat. There are 13 solved examples and 12 exercises.
Elastic problems for the half-space and circular cylinders are discussed in Chapter 3. Sections 2 and 3 list the stress-strain relations and the equations of motion. Section 4 lists the Papkovitch-Neuber functions and the differential equations satisfied by them. Sections 5–13 present the solutions to the fundamental problems of determining stress and displacement fields due to concentrated point, line, or distributed sources. Section 14 contains solved examples of plain strain due to a load on a finite strip on the bounding plane of the half-space. Section 15 lists some Fourier integral formulas and 16 contains the application of Fourier transform for several half-space problems. In Section 17, solutions to plane strain problems due to surface loading have been presented. Section 18 is on plane strain problems due to moving surface loads, and Section 19 contains solutions to the plane strain problem of a hollow circular cylinder. Sections 20–29 are concerned with problems arising due to indentation on the bounding plane of the half-space, flat-ended smooth cylinders, and rigid spheres. An integral equation approach is used for solving indentation problems. Some typical integral equations and their solutions are given in an appendix. There are 39 examples and 25 exercises in this chapter.
Chapter 4 gives a short account of thermoelasticity. This chapter contains general solutions for a 2D steady state thermoelastic problem for the half-space, the inertia effects in a half-space problem, the effect of coupling of displacement and temperature, and both the 2D and 3D steady state thermoelastic problem for the half-space due to a moving heat source.
Viscoelasticity is the subject of Chapter 5. The basic stress-strain relations of various models viz the Hookien, Kelvin-Voigt, Maxwell, and finally the Boltzmann and Biot are given in Section 2. Section 3 contains the well-known analogy between elasticity and viscoelasticity. Section 4 contains the integral form of stress-strain relationships for viscoelastic materials. Temperature effects are discussed in the next section. Sections 6–9 present solutions of some standard problems in viscoelasticity. The last section gives a reference to the problem of a multilayered viscoelastic media under a moving load.
The next chapter is on perfect plasticity. Slip-Line theory is discussed in Section 2. The rest of the sections, 17 in all, contain concepts or solutions to problems in plasticity: stress distribution in a semi-infinite solid under a lubricated flat punch, stress distribution in a truncated wedge under a lubricated flat punch, stress field in a wedge under lateral pressure, compression of a wedge by a flat die, sliding of a wedge under a flat die under load indentation of a semi-infinite solid by a lubricated wedge, a friction model, friction of ploughing by rigid asperities, different regimes of friction and wear, indentation of sandwich metal strips between flat dies, oblique impact of a hard ball against a ductile solid, slip-line field of the rolling contact problem at high loads, indentation of a semi-infinite solid by a cylinder, flattening of circular cylinder by a lubricated die, indentation of a semi-infinite solid by a spherical die, indentation of a semi-infinite solid by the end of a lubricated cylinder, and entation of a semi-infinite solid by a lubricated truncated cone.
Chapter 7 contains a brief discussion on rough surfaces. It includes bearing area curves, profilometric representation of surfaces, characterization of surfaces by auto correlation functions, characterization of surfaces by actual area of contact, characterization of surfaces by compliance, characterization of surfaces by fractal geometry, and the chapter ends by describing some studies involving surface textures.
Applications are discussed in the last chapter. Starting with a section on Blok’s conjecture, the chapter contains a total of 26 solutions to a variety of problems including one concerning couple stress. The last nine sections are devoted to the following topics: deformation friction, 2D rolling in viscoelastic material, contact problems in linear theory of viscoelasticity, thermal softening of mechanism of fading of lubricated brakes and clutches, plastic shakedown in rolling contact, soft metals in static and dynamic loading and friction under metalworking process, contact between rough surfaces with longitudinal texture, transient temperatures in the vicinity of an asperity contact, and the normal impact model of rough surfaces.
In view of the large number of solutions to basic problems in diverse areas of solid mechanics, Fundamentals of Surface Mechanics with Applications is a valuable resource for both researchers and students in solid mechanics. It is recommended for libraries of educational institutions with a program in engineering and research institutions where research in solid mechanics is carried out.