This book is devoted to the (nonlinear) behaviour of materials described by an intermediate theory lying between the discrete representation and the continuum one of the matter. It is clear from this fact that a dispersive behaviour of materials appears which is responsible for many interesting phenomena, such as solitary wave, shock waves and so on. This study is carried out on three levels of understanding and representing the reality: physics, applied mathematics, and numerics. As the author writes, the researcher has a mental comfort when numerical simulations give results predicted by the constructed theory. In order to inform the reader about the topics covered in this original book, we list the contents: (1) Different types of crystals; (2) Discrete and continuum descriptions: general introduction; (3) Elasticity and anelasticity: continuous viewpoint; (4) Elasticity and anelasticity: discrete viewpoint; (5) Coupled fields in elasticity; (6) Nonlinear waves in elastic chains; (7) Nonlinear waves in elastic crystals with a microstructure; (8) Nonlinear waves in martensite structures; (9) Nonlinear acoustic surface waves in crystals; (10) Shock waves and phase-transition fronts in thermoelastic crystals; (11) Miscellany; (12) Summary and conclusions; Appendices; Bibliography; Subject index.
The book has a clearly printed text, with spaces allowing to distinguish the figures and the equations. As to the illustrations, these consist almost entirely of images of singular surfaces in materials, and of numerical graphs produced by the use of computational tools (such as MATLAB and MATHEMATICA). The references contain a lot of papers and books concerning the material. Apart from the immediate content, each section contains very interesting comments of the author on the history and on the state-of-the-art of the topics discussed. Thus the book makes the reader familiar with the way in which the scientific truth was gradually attained. In the reviewer’s opinion, the volume is worthy to be studied, and then to be re-read.