Continua with Microstructure

This book proposes a new general setting for theories of bodies with microstructure when they are described within the scheme of the con­ tinuum: besides the usual fields of classical thermomechanics (dis­ placement, stress, temperature, etc.) some new fields enter the picture (order parameters, microstress, etc.). The book can be used in a semester course for students who have already followed lectures on the classical theory of continua and is intended as an introduction to special topics: materials with voids, liquid crystals, meromorphic con­ tinua. In fact, the content is essentially that of a series of lectures given in 1986 at the Scuola Estiva di Fisica Matematica in Ravello (Italy). I would like to thank the Scientific Committee of the Gruppo di Fisica Matematica of the Italian National Council of Research (CNR) for the invitation to teach in the School. I also thank the Committee for Mathematics of CNR and the National Science Foundation: they have supported my research over many years and given me the opportunity to study the topics presented in this book, in particular through a USA-Italy program initiated by Professor Clifford A. Truesdell. My interest in the field dates back to a period of collaboration with Paolo Podio-Guidugli and some of the basic ideas came up during our discussions. The book offers a new general setting for theories of bodies with microstructure (or ordered media as they are also called) when they are described within the scheme of the Continuum: then besides the usual fields of classical thermomechanics (displacement, stress, temperature, etc.) some new fields enter the picture (order parameters, microstress, etc.). The book can be used in a semester course for students who have followed already lectures on the classical theory of continua as an introduction to special topics: materials with voids, liquid crystals, meromorphic continua (all topics that are briefly mentioned here as examples). Research students studying continuum theories of new materials will find the book of help, as it may offer the appropriate framework for new developments and a link between apparently disparate themes such as the topological theory of defects, phase transitions and boojums. Front Matter....Pages i-x Introduction....Pages 1-4 General Properties....Pages 5-41 Special Theories....Pages 42-66 Thermodynamics....Pages 67-76 Mathematical Problems Posed by the Theory....Pages 77-89 Back Matter....Pages 90-93