9R12. Creep Mechanics. - J Betten (Dept of Math Models in Mat Sci, Tech Univ Aachen, Augustinerbach 4-22, Aachen, 52064, Germany). Springer-Verlag, Berlin. 2002. 327 pp. ISBN 3-540-42981-6. $89.95.
Reviewed by NCM Tsang (Dept of Civil and Env Eng, Imperial Col of Sci, Tech and Med, London, SW7 2BU, UK).
This textbook covers both the fundamentals and application of mathematical modeling of material behavior under creep conditions using tensor function theory. The book is based on the author’s lectures and research publications since 1969. In addition to solid mechanics, the book also covers the analysis of linear and nonlinear viscous fluids. An example of creep damage analysis of thick-walled tubes is provided. The book’s level is directed as a text for graduate students and as a reference for professional practitioners and researchers in the area of time-dependent structural stress and deformation analysis.
The book consists of 13 chapters and two appendices. Current advancement in the area of creep and creep rupture is first reviewed among a broader theme of damage mechanics. A description of the tensor function theory and its general bases are given in Chapter 2. This enables the readers to get a grip on the mathematics adopted throughout the book. The basics of the continuum mechanics are presented in Chapter 3. This provides a framework of basic equations for material modeling and demonstrates the need of additional equations to characterize the time-dependent behavior of particular material. These three chapters introduce the fundamental knowledge that is required to study the rest of the book. The chapters should be particularly helpful to post-graduate students.
In Chapter 4, basic modeling techniques of creep behavior in primary, secondary, and tertiary stages are explained. The creep potential hypothesis is presented. A case study on creep behavior of thick-walled tubes is discussed in Chapter 5. The creep potential hypothesis is compared with the tensor function theory in Chapter 6. The variations in modeling isotropic and anisotropic material are discussed. Chapter 7 deals with creep damage and the use of damage tensors. Tensorial generalization of uniaxial creep laws to multiaxial states of stress is illustrated in Chapter 8.
The book then goes on to discuss viscous fluids: linear and nonlinear in Chapters 9–12. Particular attention is given to various viscoelastic rheological models including Maxwell, Kelvin, and Burgers models in Chapter 11. Here, the MAPLE computer program codes of various functions and their results are illustrated. The parametric studies using the MAPLE computer program demonstrate the sensitivities of various parameters of the proposed numerical models. This strengthens the readers’ understanding of and confidence in using the models. Viscoplastic materials are briefly explained in Chapter 12. The discussion of creep experiments in Chapter 13 is interesting, and the references of various creep tests are especially useful for researchers. The two appendices detailing the Dirac and Heaviside functions (Appendix A) and Laplace transformations (Appendix B) provide a very useful reference for readers who are not equipped with this type of mathematical skill for creep analysis.
Derivatives for numerical models and algorithms for numerical methods are presented in a very clear manner. This is particularly helpful in clarifying many issues that are presented in an abstract form in other books. The generalization techniques of uniaxial creep laws to handle multiaxial stress states and the highlight of differences in modeling isotropic and anisotropic materials are essential for engineers analyzing modern structures. The figures (72 in total) are clear and of great help in promoting the readers’ understanding. Although only one major example covering thick-wall tubes is given, it is adequate in promoting the understanding of this complex modeling technique. For students, the appendices detailing the Dirac and Heaviside functions and Laplace transformations are particularly useful. In conclusion, the style is clear and to the point.
This reviewer enjoyed reading Creep Mechanics and recommends it for research students and practitioners alike.