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Continua with Microstructure

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概要 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.続きを見る
目次 {sect}1 Introduction
I General Properties
{sect}2 The Model for the Microstructure
{sect}3 The Notion of Observer
{sect}4 Continua with Microstructure
{sect}5 Invariance Properties
{sect}6 Conservation of Mass: Kinetic Energy
{sect}7 Inertia
{sect}8 Dynamic Equations of Balance
{sect}9 Balance of Moment of Momentum
{sect}10 Boundary Conditions: Change of Variables
{sect}11 The Conservative Case in Statics
{sect}12 Perfect Fluids with Microstructure
{sect}13 Rules of Invariance and the Balance of Moment of Momentum: Variational Principles in Dynamics
{sect}14 Internal Constraints: Continua with Latent Microstructure
II Special Theories
{sect}15 Continua with One-Dimensional Microstructure: Continua with Voids
{sect}16 Liquids with Bubbles
{sect}17 Dilatant Granular Materials
{sect}18 The Perfect Korteweg Fluid
{sect}19 Continua with Vectorial Microstructure
{sect}20 Uniaxial Liquid Crystals
{sect}21 Continua with Affine Microstructure
{sect}22 Micromorphic Elastic Continua: Bodies with Continuous Distribution of Dislocations
{sect}23 The Continua of Cosserat
{sect}24 Biaxial Nematic Liquid Crystals
III Thermodynamics
{sect}25 Balance Equations
{sect}26 Interpretation of the Equations of Balance
{sect}27 Thermodynamics of Continua with Latent Microstructure
{sect}28 Comparison with the Traditional Class of Hyperelastic Bodies
IV Mathematical Problems Posed by the Theory
{sect}29 The Influence of the Topological Properties of the Manifold M
{sect}30 Further Remarks on the Topological Theory of Defects
{sect}31 Existence of Singular Solutions in Statics
{sect}32 Phase Transitions
{sect}33 Droplets of Perfect Liquids with Microstructure.
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登録日 2020.06.27
更新日 2020.06.28