Composite materials :mathematical theory and exact relations /

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"Version: 20250601"--Title page verso.Includes bibliographical references.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. The compensated compactness property -- 2.6. Geometry of local spaces3. Composite materials -- 3.1. Mathematical definition of a composite -- 3.2. Periodic composites -- 3.3. Properties of H-convergencepart 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, 4.11, 4.135. Links -- 5.1. Links as exact relations -- 5.2. Algebraic structure of links -- 5.3. Volume fraction formulas as links6. 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 linkspart III. Case studies. 7. Introduction -- 8. Conductivity with Hall effect -- 8.1. 2D conductivity with Hall effect -- 8.2. 3D conductivity with Hall effect -- 8.3. Fibrous conducting composites with Hall effect9. Elasticity -- 9.1. 2D elasticity -- 9.2. 3D elasticity -- 9.3. Fibrous elastic composites10. Piezoelectricity -- 10.1. Exact relations -- 10.2. Links -- 10.3. 2D-specific relations and links11. Thermoelasticity -- 11.1. 2D Thermoelasticity -- 11.2. 3D Thermoelasticity12. Thermoelectricity -- 12.1. Equations of thermoelectricity -- 12.2. Seebeck effect -- 12.3. The canonical form of equations of thermoelectricity -- 12.4. 2D Thermoelectricity -- 12.5. 3D Thermoelectricitypart IV. Appendices. 13. Closedness of E(B1) and J(B1) for conductivity and elasticity -- 13.1. Conductivity -- 13.2. Elasticity14. Characterization of all global Jordan isomorphisms of Sym(T) -- 15. Jordan subalgebras of real symmetric matrices -- 15.1. Questions about real n x n matrices -- 15.2. Structure of Jordan subalgebras of Sym(Rn) -- 15.3. Simple, irreducible Jordan subalgebras of Sym(Rn) -- 15.4. Reflexivity of Jordan subalgebras of Sym(Rn)16. A polycrystalline L-relation that is not exact -- 17. Multiplication of SO(3) irreps in endomorphism algebras -- 17.1. Irreducible representations (irreps) of SO(3) -- 17.2. Raising and lowering operators -- 17.3. Homogeneous coordinates of irreps in endomorphism algebras -- 17.4. Clebsch-Gordan coefficients -- 17.5. Choice structure coefficients -- 17.6. The Racah coefficients -- 17.7. Multiplication of irreps in End(V) -- 17.8. Example : choice structure constants for piezoelectricity.Full-text restricted to subscribers or individual document purchasers.This extended and updated new edition captures developments and results since the original edition and includes a new chapter on two-dimensional thermoelectricity, which concerns itself with effects coupling thermal and electrical conduction in the media. The book starts with a novel unified approach to homogenization, and develops a general theory of microstructure-independent (exact) relations for composite materials that applies to most physical properties of interest, such as conductivity, elasticity, piezoelectricity, thermoelectricity etc. Its methods allow one to obtain a complete list of exact relations in each physical context of interest.Professional and scholarly.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Yury Grabovsky is a professor at the Department of Mathematics at Temple University, where his research interests include the calculus of variations on the mathematics side and continuum mechanics on the physics side. His latest work was on the mathematical theory of composite materials, the buckling of slender bodies, such as plates, rods, and shells, and understanding the stability of equilibrium configurations with phase boundaries in nonlinear elasticity. After graduating with a PhD from the Courant Institute of Mathematical Sciences, New York University, Yury spent a year as a postdoc at the Center for Nonlinear Analysis at Carnegie Mellon University, and three years as a Wylie Instructor at the University of Utah. In 1999 he was hired as a tenure-track Assistant Professor by Temple University. Yury enjoys teaching and performing research with students. His webpage on using continued fractions in the design of calendar systems routinely draws the attention of media every leap year. It has been translated into Portuguese and published in a journal for mathematics schoolteachers Educa?c?aao e Matem?atica.Title from PDF title page (viewed on July 1, 2025).

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: .,

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1 online resource (various pagings) :illustrations (some color).

Language

English

ISBN/ISSN

9780750362498

Classification

620.118

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Edition

Second edition.

Subject(s)

SCIENCE / Physics / Mathematical & Computational.
Composite materials.
Materials science
Mathematical physics.

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Yury Grabovsky.

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