Overview	6
	Readers Guidance	7
	Contents	9
	1 Introduction	14
	1.1 Objectives of This Work	17
	1.1.1 Summary of Composites Considered	18
	2 Classification of Composites	19
	2.1 Volume Concentrations	19
	2.2 Geometry at Fixed Phase Concentrations	20
	2.2.1 Geometrical Classification	21
	2.3 Composites with Variable Geometry	22
	2.3.1 Geometrical Classification	22
	2.3.2 Some Composite Examples	26
	3 Preliminaries on Stress/Strain	29
	3.1 Stiffness	29
	3.1.1 Dilute Suspension	31
	3.2 Stress	32
	3.3 Composite Sti.ness Estimated by SCS	32
	4 Composite Stress and Geometry	35
	4.1 Volumetric Stress	35
	4.1.1 CSA-Composites	35
	4.1.2 Any Composite – Geometry Function	36
	4.1.3 Geometry Function and Shape Function	37
	4.1.4 Shape Functions – A Closer Look	39
	4.1.5 Summary	42
	4.2 Deviatoric Stress	43
	4.2.1 Stress and Geometry	43
	4.3 Summary on Stress and Geometry	44
	4.3.1 Stress	44
	4.3.2 Geo-Function	44
	5 Composite Stiffness and Geometry	46
	5.1 Bulk Modulus and Shear Modulus	46
	5.1.1 Porous Materials and Stiff Pore Systems	46
	5.2 Young’s Modulus and Poisson’s Ratio	47
	5.3 Special Composites and Observations	47
	5.3.1 CSA-Composites	48
	5.3.2 Composites with Special Shear Moduli Geo-Independent Bulk Moduli	48
	5.3.3 Paul/Hansen versus Geo-Functions	49
	6 Composite Eigenstrain/Stress	50
	6.1 Basics	50
	6.1.1 Simple Composites	51
	6.2 General Geometry	51
	6.2.1 Eigenstrain and Eigenstress	51
	6.2.2 Pore Pressure in Porous Materials	52
	7 Quantification of Geometry	53
	7.1 Shape Factors	57
	7.1.1 DC-Composites	57
	7.1.2 CD-Composites	63
	7.1.3 MM-Composites	64
	7.2 Shape Functions and Geo-Path	67
	7.2.1 Default	67
	7.2.2 Alternative I	70
	7.2.3 Alternative II	71
	7.3 Geo-Paths	72
	8 Composite Theory – Elasticity	74
	8.1 Illustrative Examples	74
	8.1.1 DC-CD Composite	74
	8.1.2 Crumbled Foils Composite	76
	8.1.3 Particulate (DC-DC) Composite	78
	8.2 Other Examples	80
	8.2.1 Cracks	80
	8.2.2 Special DC-CD Composites Isotropy	84
	8.3 FEM-Analysis versus Theory	87
	8.3.1 FEM-Analysis	87
	8.3.2 Particulate Composite	89
	8.3.3 Defective Particulate Composite	91
	8.3.4 Pearls on a String Composite	96
	8.3.5 Grid Composite	100
	8.3.6 Cracked Material	103
	8.3.7 Discussion of FEM-Analysis	104
	8.4 Conclusion	107
	9 Composite Theory – Conductivity	108
	9.1 Theory	108
	9.2 Illustrative Examples	109
	9.2.1 Porous Materials and Stiff Pore Systems	109
	9.2.2 Dilute Porous Materials and Stiff Pore Systems	111
	9.2.3 Cracked Materials (Soft and Stiff Cracks)	111
	9.2.4 Crumbled Foils Composite	113
	9.3 Theory versus Experiments	113
	9.3.1 Chloride Diffusion in HCP and HCP with Silica Fume	113
	9.3.2 Thermal Conductivity of Plane-Isotropic Fiber Composite	116
	9.4 Theory versus SCS-Estimates	118
	9.5 Conclusion	118
	10 Simplified Composite Theory – Elasticity	121
	10.1 Basis of Analysis	123
	10.1.1 Geometry	123
	10.1.2 Quantification of Composite Geometry	125
	10.1.3 Preparation of Composite Analysis	129
	10.2 Analysis	130
	10.2.1 Bounds and Other Accurate Stiffness Expressions	131
	10.2.2 Test of Theory	131
	10.3 Illustrative Examples	133
	10.3.1 Composites with Spherical Particles (CSAP)	134
	10.3.2 Nearly CSAP Composites	134
	10.3.3 Phase Symmetric Composites	135
	10.3.4 Eigenstrain/Stress versus Geometry	140
	10.3.5 Porous Materials	140
	10.4 Theory and Experiments	145
	10.4.1 Some Irregular Geometries Non-Flexible Geometry – Interference	145
	10.4.2 Various Porous Materials	148
	10.4.3 Sulphur Impregnated Cement/Silicate System	152
	10.4.4 Salt Infected Bricks	154
	10.4.5 Non-Flexible Particles in Particulate Composite	155
	10.4.6 Defective Phase Contact in Concrete	157
	10.4.7 Hydrating Cement Paste and Concrete	159
	10.5 Conclusion	162
	11 Simplified Composite Theory – Conductivity	163
	11.1 Illustrative Example	163
	11.1.1 On the Accuracy of Simplification	164
	11.2 Applications	164
	11.2.1 Thermal Conductivity of Fire-Brick	164
	11.2.2 Electrical Conductivity of Binary Metallic Mixtures	164
	11.2.3 Chloride Di.usion in Cement Paste System	166
	11.3 Conclusion	169
	12 Diagnostic Aspects of Theory	170
	12.1 Stiffness	172
	12.1.1 Examination of Sti.ness Expressions Isotropy Check	172
	12.2 Conductivity	178
	12.2.1 Examination of SCS-Expressions Spheres: Böttcher/ Landauer	178
	12.3 Discussion	181
	13 Aspects of Materials Design	184
	13.1 Geometries versus Properties	184
	13.2 Design	185
	13.3 Illustrative Examples	185
	13.3.1 Stiffness	185
	13.3.2 Conductivity	187
	13.4 Discussion	189
	14 Viscoelasticity	190
	14.1 Stress-Strain Relations	191
	14.1.1 Analogy Young’s Modulus	192
	14.1.2 Vibrations	194
	14.2 Models of Viscoelastic Materials	196
	14.2.1 Simple Models	197
	14.2.2 Less Simple Models	197
	14.3 Summary, Analysis, and Approximate Analysis	202
	14.3.1 Approximate Analysis	203
	15 Viscoelastic Composites	206
	15.1 Composite Analysis	207
	15.1.1 Accurate Analysis	207
	15.1.2 Approximate Analysis	207
	15.2 Applications	209
	15.2.1 Porous Materials and Stiff Pore Systems	210
	15.2.2 Particulate Composite	210
	15.2.3 Mature Cement Concrete	211
	15.2.4 Young Concrete	217
	15.2.5 In.uence of Geometry on Viscoelastic Composite Behavior Particulate Composite versus Grid Reinforced Composite	217
	15.2.6 Monomer Impregnated HCP and Porous Glass	222
	15.2.7 Damping of Wood	225
	15.3 Discussion	227
	16 Final Remarks	228
	A Elasticity	230
	A.1 Isotropy	230
	A.1.1 Composite Aspects	230
	A.1.2 Stress-Strain	230
	A.2 Cubic Elasticity	231
	A.2.1 Poly-Cubic Elasticity	232
	A.2.2 Composite Aspects	233
	B Dilute Particulate Composites	234
	B.1 Cubic Stiffness, Shape Parameters, and Stress	234
	B.1.1 Particle Stress	235
	B.1.2 Isotropic Stiffness, Shape Coefficients, and Stress	237
	B.1.3 Particle Stress	237
	C SCS-Analysis	238
	C.1 Stiffness	238
	C.1.1 Spherical Particles	239
	C.1.2 Various Particle Shapes and Cracks	240
	C.1.3 Multi-Shaped Particles	241
	C.2 Other Physical Properties	242
	C.2.1 Spherical Particles	243
	C.2.2 Particles of Various Shapes and Cracks	243
	C.2.3 Multi-Shaped Particles	245
	D General Viscoelastic Models	246
	E HCP and Concrete	248
	E.1 Volume Models	248
	E.2 Porosity of Hardening Cement Paste	249
	Notations	251
	References	254