TY - BOOK
AU - Grabovsky,Yury
ED - Institute of Physics (Great Britain),
TI - Composite materials: mathematical theory and exact relations
T2 - [IOP release 3]
SN - 9780750310482
AV - TA418.9.C6 G733 2016eb
U1 - 620.118 23
PY - 2016///]
CY - Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK)
PB - IOP Publishing
KW - Composite materials
KW - Materials science
KW - Mathematics
KW - Mathematical physics
KW - bicssc
KW - SCIENCE / Physics / Mathematical & Computational
KW - bisacsh
N1 - "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; Researchers and graduate students in physics, materials science and engineering; Also available in print
N2 - 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
UR - https://iopscience.iop.org/book/978-0-7503-1048-2
ER -