The classical theories of Linear Elasticity and Newtonian Fluids, though trium phantly elegant as mathematical structures, do not adequately describe the defor mation and flow of most real materials. Attempts to characterize the behaviour of real materials under the action of external forces gave rise to the science of Rheology. Early rheological studies isolated the phenomena now labelled as viscoelastic. Weber (1835, 1841), researching the behaviour of silk threats under load, noted an instantaneous extension, followed by a further extension over a long period of time. On removal of the load, the original length was eventually recovered. He also deduced that the phenomena of stress relaxation and damping of vibrations should occur. Later investigators showed that similar effects may be observed in other materials. The German school referred to these as "Elastische Nachwirkung" or "the elastic aftereffect" while the British school, including Lord Kelvin, spoke ofthe "viscosityofsolids". The universal adoption of the term "Viscoelasticity", intended to convey behaviour combining proper ties both of a viscous liquid and an elastic solid, is of recent origin, not being used for example by Love (1934), though Alfrey (1948) uses it in the context of polymers. The earliest attempts at mathematically modelling viscoelastic behaviour were those of Maxwell (1867) (actually in the context of his work on gases; he used this model for calculating the viscosity of a gas) and Meyer (1874).

This monograph consists of two volumes and provides a unified, comprehensive presentation of the important topics pertaining to the understanding and determination of the mechanical behaviour of engineering materials under different regimes of loading. The large subject area is separated into eighteen chapters and four appendices, all self-contained, which give a complete picture and allow a thorough understanding of the current status and future direction of individual topics. Volume I contains eight chapters and three appendices, and concerns itself with the basic concepts pertaining to the entire monograph, together with the response behaviour of engineering materials under static and quasi-static loading. Thus, Volume I is dedicated to the introduction, the basic concepts and principles of the mechanical response of engineering materials, together with the relevant analysis of elastic, elastic-plastic, and viscoelastic behaviour. Volume II consists of ten chapters and one appendix, and concerns itself with the mechanical behaviour of various classes of materials under dynamic loading, together with the effects of local and microstructural phenomena on the response behaviour of the material. Volume II also contains selected topics concerning intelligent material systems, and pattern recognition and classification methodology for the characterization of material response states. The monograph contains a large number of illustrations, numerical examples and solved problems. The majority of chapters also contain a large number of review problems to challenge the reader. The monograph can be used as a textbook in science and engineering, for third and fourth undergraduate levels, as well as for the graduate levels. It is also a definitive reference work for scientists and engineers involved in the production, processing and applications of engineering materials, as well as for other professionals who are involved in the engineering design process.

Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found ana

Elastomers are found in many applications ranging from technology to daily life applications for example in tires, drive systems, sealings and print rollers. Dynamical operation conditions put extremely high demands on the performance and stability of these materials and their elastic and flow properties can be easily adjusted by simple manipulations on their elastic and viscous properties. However, the required service life suffers often from material damage as a result of wear processes such as abrasion and wear fatigue, mostly caused by crack formation and propagation. This book covers interdisciplinary research between physics, physical chemistry, material sciences and engineering of elastomers within the range from nanometres to millimetres and connects these aspects with the constitutive material properties. The different chapters describe reliable lifetime and durability predictions based on new fracture mechanical testing concepts and advanced material-theoretical methods which are finally implemented in the finite element method for structural simulations. The use of this approach allows a realistic description of complex geometrical and loading conditions which includes the peculiarities of the mechanical behaviour of elastomeric materials in detail. Furthermore, this approach demonstrates how multi-scale research concepts provide an ambitious interdisciplinary challenge at the interface between engineering and natural sciences. This book covers the interests of academic researchers, graduate students and professionals working in polymer science, rubber and tire technology and in materials science at the interface of academic and industrial research.