Composite materials : mathematical theory and exact relations /
Grabovsky, Yury,
Composite materials : mathematical theory and exact relations / Yury Grabovsky. - 1 electronic document (various pagings) : color illustrations. - [IOP release 3] IOP expanding physics, 2053-2563 . - IOP (Series). Release 3. IOP expanding physics. .
"Version: 20161201"--Title page verso.
Includes bibliographical references.
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.
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.
Researchers and graduate students in physics, materials science and engineering.
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.
9780750310482 9780750311151
10.1088/978-0-7503-1048-2 doi
Composite materials.
Materials science--Mathematics.
Mathematical physics.
SCIENCE / Physics / Mathematical & Computational.
TA418.9.C6 / G733 2016eb
620.118
Composite materials : mathematical theory and exact relations / Yury Grabovsky. - 1 electronic document (various pagings) : color illustrations. - [IOP release 3] IOP expanding physics, 2053-2563 . - IOP (Series). Release 3. IOP expanding physics. .
"Version: 20161201"--Title page verso.
Includes bibliographical references.
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.
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.
Researchers and graduate students in physics, materials science and engineering.
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.
9780750310482 9780750311151
10.1088/978-0-7503-1048-2 doi
Composite materials.
Materials science--Mathematics.
Mathematical physics.
SCIENCE / Physics / Mathematical & Computational.
TA418.9.C6 / G733 2016eb
620.118