Composite materials : mathematical theory and exact relations /

Composite materials : mathematical theory and exact relations /

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Bibliographic Details
Author / Creator:Grabovsky, Yury, author.
Imprint:Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2016]
Description:1 electronic document (various pagings) : color illustrations.
Language:English
Series:IOP expanding physics, 2053-2563
[IOP release 3]
IOP expanding physics.
IOP (Series). Release 3.
Subject:
Materials science -- Mathematics.
Composite materials.
Composite materials.
Materials science -- Mathematics.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11319987
Hidden Bibliographic Details
Other authors / contributors:Institute of Physics (Great Britain), publisher.
ISBN:9780750310499
9780750311151
9780750310482
Notes:"Version: 20161201"--Title page verso.
Includes bibliographical references.
Also available in print.
System requirements: Adobe Acrobat Reader, EPUB reader. or Kindle reader.
Yury Grabovsky is an associate professor in the Department of Mathematics in the College of Science and Technology at Temple University, Philadelphia, USA.
Title from PDF title page (viewed on January 13, 2017).
Summary: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.
Target Audience:Researchers and graduate students in physics, materials science and engineering.
Other form:Print version: 9780750310499
Standard no.:10.1088/978-0-7503-1048-2
Table of Contents:
  • 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
  • Preface
  • 1. Introduction
  • part I. Mathematical theory of composite materials
  • 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

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