000			03300nam a22003017a 4500
003			ZW-GwMSU
005			20230829113652.0
008			230829b |||||||| |||| 00| 0 eng d
020			_a9780750310499
040			_arda _bEnglish _cMSULIB _erda
050			_aTA418.9.C6 GRA
100	1		_aGrabovsky Yury _eauthor
245	1	0	_aComposite materials : _bmathematical theory and exact relations / _ccreated by Yury Grabovsky
264			_bIOP Publishing, _c2016.
300			_axiv, (irregular pagination): _c25 cm
336			_2rdacontent _atext
337			_2rdamedia _aunmediated _bn
338			_2rdacarrier _avolume _bnc
504			_aIncludes a bibliography
505			_a 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
520			_aThe 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
650		0	_aComposite materials
650		0	_aMaterials science _xMathematics
650		0	_aPhysics _xMathematical & Computational
650		0	_aMathematical physics
650		0	_aComposites
942			_2lcc _cB
999			_c163096 _d163096