Continua with microstructure
Author(s)
Bibliographic Information
Continua with microstructure
（Springer tracts in natural philosophy, v. 35）
Springer-Verlag, c1989
- : us
- : gw
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Note
"Lectures given in 1986 at the Scuola Estiva di Fisica Matematica in Ravello (Italy)" -- Pref
Description and Table of Contents
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.
Table of 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.
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