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Full Description
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.
Contents
§1 Introduction.- I General Properties.- §2 The Model for the Microstructure.- §3 The Notion of Observer.- §4 Continua with Microstructure.- §5 Invariance Properties.- §6 Conservation of Mass: Kinetic Energy.- §7 Inertia.- §8 Dynamic Equations of Balance.- §9 Balance of Moment of Momentum.- §10 Boundary Conditions: Change of Variables.- §11 The Conservative Case in Statics.- §12 Perfect Fluids with Microstructure.- §13 Rules of Invariance and the Balance of Moment of Momentum: Variational Principles in Dynamics.- §14 Internal Constraints: Continua with Latent Microstructure.- II Special Theories.- §15 Continua with One-Dimensional Microstructure: Continua with Voids.- §16 Liquids with Bubbles.- §17 Dilatant Granular Materials.- §18 The Perfect Korteweg Fluid.- §19 Continua with Vectorial Microstructure.- §20 Uniaxial Liquid Crystals.- §21 Continua with Affine Microstructure.- §22 Micromorphic Elastic Continua: Bodies with Continuous Distribution of Dislocations.- §23 The Continua of Cosserat.- §24 Biaxial Nematic Liquid Crystals.- III Thermodynamics.- §25 Balance Equations.- §26 Interpretation of the Equations of Balance.- §27 Thermodynamics of Continua with Latent Microstructure.- §28 Comparison with the Traditional Class of Hyperelastic Bodies.- IV Mathematical Problems Posed by the Theory.- §29 The Influence of the Topological Properties of the Manifold M.- §30 Further Remarks on the Topological Theory of Defects.- §31 Existence of Singular Solutions in Statics.- §32 Phase Transitions.- §33 Droplets of Perfect Liquids with Microstructure.
