Composite materials
mathematical theory and exact relations
Grabovsky, Yury
creator
author.
Institute of Physics (Great Britain)
publisher.
text
bibliography
enk
2016
monographic
eng
access
1 electronic document (various pagings) : color illustrations.
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.
Preface -- 1. Introduction -- part I. Mathematical theory of composite materials
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
3. Composite materials -- 3.1. Mathematical definition of a composite -- 3.2. Periodic composites -- 3.3. Properties of H-convergence
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
5. Links -- 5.1. Links as exact relations -- 5.2. Algebraic structure of links -- 5.3. Volume fraction formulas as links
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
part III. Case studies -- 7. Introduction
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
9. Elasticity -- 9.1. Two-dimensional elasticity -- 9.2. Three-dimensional elasticity -- 9.3. Fibrous elastic composites
10. Piezoelectricity -- 10.1. Exact relations -- 10.2. Links -- 10.3. Two-dimension-specific relations and links
11. Thermoelasticity -- 11.1. Two-dimensional thermoelasticity -- 11.2. Three-dimensional thermoelasticity -- 12. Three-dimensional thermoelectricity
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.
Researchers and graduate students in physics, materials science and engineering.
Yury Grabovsky.
"Version: 20161201"--Title page verso.
Includes bibliographical references.
Also available in print.
Mode of access: World Wide Web.
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.
Composite materials
Materials science
Mathematics
Mathematical physics
SCIENCE / Physics / Mathematical & Computational
TA418.9.C6 G733 2016eb
620.118
IOP (Series)
Release 3
IOP expanding physics
9780750310482
9780750311151
https://iopscience.iop.org/book/978-0-7503-1048-2
https://iopscience.iop.org/book/978-0-7503-1048-2
CaBNVSL
161207
20220822104602.0
9780750310482
eng