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.

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.