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Composite materials
Title statement Composite materials : mathematical theory and exact relations / Yury Grabovsky. [elektronický zdroj] Publication Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2016] Phys.des. 1 electronic document (various pagings) : color illustrations. ISBN 9780750311151 mobi 9780750310482 (online) Edition IOP expanding physics, ISSN 2053-2563 [IOP release 3] Note "Version: 20161201"--Title page verso. Internal Bibliographies/Indexes Note Includes bibliographical references. Contents Preface -- 1. Introduction -- part I. Mathematical theory of composite materials Content note 11. Thermoelasticity -- 11.1. Two-dimensional thermoelasticity -- 11.2. Three-dimensional thermoelasticity -- 12. Three-dimensional thermoelectricity. 10. Piezoelectricity -- 10.1. Exact relations -- 10.2. Links -- 10.3. Two-dimension-specific relations and links. 9. Elasticity -- 9.1. Two-dimensional elasticity -- 9.2. Three-dimensional elasticity -- 9.3. Fibrous elastic composites. 8. Conductivity with the Hall effect -- 8.1. Two-dimensional conductivity with the Hall effect -- 8.2. Three-dimensional conductivity with the Hall effect -- 8.3. Fibrous conducting composites with the Hall effect. part III. Case studies -- 7. Introduction. 6. Computing exact relations and links -- 6.1. Finding Jordan A-multialgebras -- 6.2. Computing exact relations -- 6.3. Computing volume fraction relations -- 6.4. Finding Jordan A^-multialgebras -- 6.5. Computing links. 5. Links -- 5.1. Links as exact relations -- 5.2. Algebraic structure of links -- 5.3. Volume fraction formulas as links. part II. General theory of exact relations and links -- 4. Exact relations -- 4.1. Introduction -- 4.2. L-relations -- 4.3. Sufficient conditions for stability under homogenization -- 4.4. Special types of exact relations -- 4.5. Proofs of theorems 4.8, 4.12, 4.11. part IV. Appendices -- A. E- and J -regularity for conductivity and elasticity -- B. A polycrystalline L-relation that is not exact -- C. Multiplication of SO(3) irreps in endomorphism algebras.. 3. Composite materials -- 3.1. Mathematical definition of a composite -- 3.2. Periodic composites -- 3.3. Properties of H-convergence. 2. Material properties and governing equations -- 2.1. Introduction -- 2.2. Conductivity and elasticity -- 2.3. Abstract Hilbert space framework -- 2.4. Boundary value problems -- 2.5. Geometry of local spaces Notes to Availability Přístup pouze pro oprávněné uživatele Audience Researchers and graduate students in physics, materials science and engineering. Note Požadavky na systém: Adobe Acrobat Reader, EPUB reader. or Kindle reader.. Způsob přístupu: World Wide Web. Another responsib. Institute of Physics (Great Britain), Subj. Headings SCIENCE / Physics / Mathematical & Computational. * Mathematical physics. * Materials science - Mathematics. * Composite materials. Form, Genre elektronické knihy electronic books Country Anglie Language angličtina Document kind Electronic books URL Plný text pro studenty a zaměstnance UPOL 
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The mathematical method of composites has reached a very high level of maturity and developments have increased our understanding of the relationship between the microstructure of composites and their macroscopic behaviour. This book provides a self-contained unified approach to the mathematical foundation of the theory of composites, leading to the general theory of exact relations. It also provides complete lists of exact relations in many specific physically relevant contexts, such as conductivity, fibre-reinforced elasticity, piezoelectricity, thermoelectricity and more.
11. Thermoelasticity -- 11.1. Two-dimensional thermoelasticity -- 11.2. Three-dimensional thermoelasticity -- 12. Three-dimensional thermoelectricity10. Piezoelectricity -- 10.1. Exact relations -- 10.2. Links -- 10.3. Two-dimension-specific relations and links9. Elasticity -- 9.1. Two-dimensional elasticity -- 9.2. Three-dimensional elasticity -- 9.3. Fibrous elastic composites8. Conductivity with the Hall effect -- 8.1. Two-dimensional conductivity with the Hall effect -- 8.2. Three-dimensional conductivity with the Hall effect -- 8.3. Fibrous conducting composites with the Hall effectpart III. Case studies -- 7. Introduction6. Computing exact relations and links -- 6.1. Finding Jordan A-multialgebras -- 6.2. Computing exact relations -- 6.3. Computing volume fraction relations -- 6.4. Finding Jordan A^-multialgebras -- 6.5. Computing links5. Links -- 5.1. Links as exact relations -- 5.2. Algebraic structure of links -- 5.3. Volume fraction formulas as linkspart II. General theory of exact relations and links -- 4. Exact relations -- 4.1. Introduction -- 4.2. L-relations -- 4.3. Sufficient conditions for stability under homogenization -- 4.4. Special types of exact relations -- 4.5. Proofs of theorems 4.8, 4.12, 4.11Preface -- 1. Introduction -- part I. Mathematical theory of composite materialspart IV. Appendices -- A. E- and J -regularity for conductivity and elasticity -- B. A polycrystalline L-relation that is not exact -- C. Multiplication of SO(3) irreps in endomorphism algebras.3. Composite materials -- 3.1. Mathematical definition of a composite -- 3.2. Periodic composites -- 3.3. Properties of H-convergence2. Material properties and governing equations -- 2.1. Introduction -- 2.2. Conductivity and elasticity -- 2.3. Abstract Hilbert space framework -- 2.4. Boundary value problems -- 2.5. Geometry of local spaces
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