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AuthorCapriz, Gianfranco. author
TitleContinua with Microstructure [electronic resource] / by Gianfranco Capriz
ImprintNew York, NY : Springer New York, 1989
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Descript X, 93 p. online resource


This book proposes a new general setting for theories of bodies with microstructure when they are described within the scheme of the conยญ tinuum: besides the usual fields of classical thermomechanics (disยญ 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 conยญ 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


ยง1 Introduction -- I General Properties -- ยง2 The Model for the Microstructure -- ยง3 The Notion of Observer -- ยง4 Continua with Microstructure -- ยง5 Invariance Properties -- ยง6 Conservation of Mass: Kinetic Energy -- ยง7 Inertia -- ยง8 Dynamic Equations of Balance -- ยง9 Balance of Moment of Momentum -- ยง10 Boundary Conditions: Change of Variables -- ยง11 The Conservative Case in Statics -- ยง12 Perfect Fluids with Microstructure -- ยง13 Rules of Invariance and the Balance of Moment of Momentum: Variational Principles in Dynamics -- ยง14 Internal Constraints: Continua with Latent Microstructure -- II Special Theories -- ยง15 Continua with One-Dimensional Microstructure: Continua with Voids -- ยง16 Liquids with Bubbles -- ยง17 Dilatant Granular Materials -- ยง18 The Perfect Korteweg Fluid -- ยง19 Continua with Vectorial Microstructure -- ยง20 Uniaxial Liquid Crystals -- ยง21 Continua with Affine Microstructure -- ยง22 Micromorphic Elastic Continua: Bodies with Continuous Distribution of Dislocations -- ยง23 The Continua of Cosserat -- ยง24 Biaxial Nematic Liquid Crystals -- III Thermodynamics -- ยง25 Balance Equations -- ยง26 Interpretation of the Equations of Balance -- ยง27 Thermodynamics of Continua with Latent Microstructure -- ยง28 Comparison with the Traditional Class of Hyperelastic Bodies -- IV Mathematical Problems Posed by the Theory -- ยง29 The Influence of the Topological Properties of the Manifold M -- ยง30 Further Remarks on the Topological Theory of Defects -- ยง31 Existence of Singular Solutions in Statics -- ยง32 Phase Transitions -- ยง33 Droplets of Perfect Liquids with Microstructure

Physics Physics Theoretical Mathematical and Computational Physics


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