Fu Y.B., Ogden R.W. (Eds.). Nonlinear Elasticity: Theory and Applications

CUP, 2001. – 535 pp. OCR. – (London Mathematical Society Lecture Note Series.283).
The subject of Finite Elasticity (or Nonlinear Elasticity), although many of its ingredients were available much earlier, really came into its own as a discipline distinct from the classical theory of linear elasticity as a result of the important developments in the theory from the late 1940s associated with Rivlin and the collateral developments in general Continuum Mechanics associated with the Truesdell school during the 1950s and 1960s. Much of the impetus for the theoretical developments in Finite Elasticity came from the rubber industry because of the importance of (natural) rubber in many engineering components, not least car tyres and bridge and engine mountings. This impetus is maintained today with an ever increasing use of rubber (natural and synthetic) and other polymeric materials in a broader and broader range of engineering products. The importance of gaining a sound theoretically-based understanding of the thermomechanical behaviour of rubber was only too graphically illustrated by the role of the rubber O-ring seals in the Challenger shuttle disaster. This extreme example serves to underline the need for detailed characterization of the mechanical properties of different rubberlike materials, and this requires not just appropriate experimental data but also the rigorous theoretical framework for analyzing those data. This involves both elasticity theory per se and extensions of the theory to account for inelastic effects.
Chapter 1 provides the basic theory required for use in the other chapters. Chapters 2-6 deal with different aspects ofthe solution of boundary-value problems for unconstrained and internally constrained materials, while Chapters 7 and 8 are concerned with the related topics of membrane theory and the theory of elastic surfaces. Chapter 9 deals with the important topic of non-uniqueness of solution using the tools of singularity theory and bifurcation theory and Chapter 10 examines some related aspects concerned with nonlinear stability analysis based on methods of perturbation theory. Nonlinear dynamics is discussed in Chapter 11, which is concerned with nonlinear wave propagation in an elastic rod. Chapters 12 and 13 are based on different notions of pseudo-elasticity theory: Chapter 12 develops a theory of phase transitions using non-convex strain-energy functions, while Chapter 13 is concerned with the effect of changing the (elastic) constitutive law during the deformation process.