UID:
almafu_9958898544302883
Format:
1 electronic document (various pagings) :
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color illustrations.
ISBN:
0-7503-1049-9
Series Statement:
IOP expanding physics,
Content:
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.
Note:
"Version: 20161201"--Title page verso.
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11. Thermoelasticity -- 11.1. Two-dimensional thermoelasticity -- 11.2. Three-dimensional thermoelasticity -- 12. Three-dimensional thermoelectricity
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10. Piezoelectricity -- 10.1. Exact relations -- 10.2. Links -- 10.3. Two-dimension-specific relations and links
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9. Elasticity -- 9.1. Two-dimensional elasticity -- 9.2. Three-dimensional elasticity -- 9.3. Fibrous elastic composites
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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
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part III. Case studies -- 7. Introduction
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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
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5. Links -- 5.1. Links as exact relations -- 5.2. Algebraic structure of links -- 5.3. Volume fraction formulas as links
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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
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Preface -- 1. Introduction -- part I. Mathematical theory of composite materials
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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.
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3. Composite materials -- 3.1. Mathematical definition of a composite -- 3.2. Periodic composites -- 3.3. Properties of H-convergence
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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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Also available in print.
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Mode of access: World Wide Web.
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System requirements: Adobe Acrobat Reader, EPUB reader. or Kindle reader.
Additional Edition:
ISBN 0-7503-1048-0
Language:
English
DOI:
10.1088/978-0-7503-1048-2
URL:
http://iopscience.iop.org/book/978-0-7503-1048-2
