Muutke küpsiste eelistusi

Capacity and Transport in Contrast Composite Structures: Asymptotic Analysis and Applications [Kõva köide]

(Universita degli Studi di Cassino, Italy), (Universita degli Studi di Cassino, Italy)
  • Formaat: Hardback, 336 pages, kõrgus x laius: 254x178 mm, kaal: 703 g, 14 Tables, black and white; 83 Illustrations, black and white
  • Ilmumisaeg: 24-Nov-2009
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1439801754
  • ISBN-13: 9781439801758
Teised raamatud teemal:
Capacity and Transport in Contrast Composite Structures: Asymptotic Analysis and ApplicationsSuurem pilt
  • Formaat: Hardback, 336 pages, kõrgus x laius: 254x178 mm, kaal: 703 g, 14 Tables, black and white; 83 Illustrations, black and white
  • Ilmumisaeg: 24-Nov-2009
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1439801754
  • ISBN-13: 9781439801758
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781439801758.html
Märksõnad:
Is it possible to apply a network model to composites with conical inclusions?How does the energy pass through contrast composites? Devoted to the analysis of transport problems for systems of densely packed, high-contrast composite materials, Capacity and Transport in Contrast Composite Structures: Asymptotic Analysis and Applications answers questions such as these and presents new and modified asymptotic methods for real-world applications in composite materials development. A mathematical discussion of phenomena related to natural sciences and engineering, this book covers historical developments and new progress in mathematical calculations, computer techniques, finite element computer programs, and presentation of results of numerical computations. The transport problem—which is described with scalar linear elliptic equations—implies problems of thermoconductivity, diffusion, and electrostatics. To address this problem, the authors cover asymptotic analysis of partial differential equations, material science, and the analysis of effective properties of electroceramics. Providing numerical calculations of modern composite materials that take into account nonlinear effects, the book also: Presents results of numerical analysis, demonstrating specific properties of distributions of local fields in high-contrast composite structures and systems of closely placed bodiesAssesses whether total flux, energy, and capacity exhaust characteristics of the original continuum modelIllustrates the expansion of the method for systems of bodies to highly filled contrast compositesThis text addresses the problem of loss of high-contrast composites, as well as transport and elastic properties of thin layers that cover or join solid bodies. The material presented will be particularly useful for applied mathematicians interested in new methods, and engineers dealing with prospective materials and design methods.

Arvustused

... deals with interesting questions of strongly heterogeneous media, such as the analysis of capacities and transport properties. ... The book is intended to be self-contained and it is of interest to researchers in the fields of "homogenization theory" and "asymptotic analysis" in the areas of applied mathematics, physics and engineering sciences. More specifically, it may be of interest to students and researchers in mathematical models related to diffusion, electricity, magnetism, mechanics, new materials and design methods. It is written in terms of electrostatics, and it pays special attention to the so-called (by the authors) "Tamm screening effect" or "Tamm shielding effect" and the problems of the "effective tunability" and "effective loss" of composite materials. These effects/terms (and some others) arising in physics and engineering are in the reviewers opinion rarely considered in the literature of applied mathematics, and the authors provide a mathematical interpretation in this book .... Many figures in the book are important for the understanding of the corresponding problems and the results obtained. Eugenia Pérez, in Mathematical Reviews, 2012a

PREFACE ix
1 IDEAS AND METHODS OF ASYMPTOTIC ANALYSIS AS APPLIED TO TRANSPORT IN COMPOSITE STRUCTURES 1
1.1 Effective properties of composite materials and the homogenization theory
2
1.1.1 Homogenization procedure for linear composite materials
3
1.1.2 Homogenization procedure for nonlinear composite materials
9
1.2 Transport properties of periodic arrays of densely packed bodies
12
1.2.1 Periodic media with piecewise characteristics and periodic arrays of bodies
12
1.2.2 Problem of computation of effective properties of a periodic system of bodies
14
1.2.3 Keller analysis of conductivity of medium containing a periodic dense array of perfectly conducting spheres or cylinders
18
1.2.4 Kozlov's model of high-contrast media with continuous distribution of characteristics. Berriman–Borcea–Papanicolaou network model
26
1.3 Disordered media with piecewise characteristics and random collections of bodies
31
1.3.1 Disordered and random system of bodies
31
1.3.2 Homogenization for materials of random structure
32
1.3.3 Network approximation of the effective properties of a high-contrast random dispersed composite
33
1.4 Capacity of a system of bodies
33
2 NUMERICAL ANALYSIS OF LOCAL FIELDS IN A SYSTEM OF CLOSELY PLACED BODIES 37
2.1 Numerical analysis of two-dimensional periodic problem
38
2.2 Numerical analysis of three-dimensional periodic problem
42
2.3 The energy concentration and energy localization phenomena
44
2.4 Which physical field demonstrates localization most strongly?
48
2.5 Numerical analysis of potential of bodies in a system of closely placed bodies with finite element method and network model
49
2.5.1 Analysis of potential of bodies belonging to an alive net
49
2.5.2 Analysis of potential of bodies belonging to an insulated net
54
2.5.3 Conjecture of potential approximation for non-regular array of bodies
54
2.6 Energy channels in nonperiodic systems of disks
55
3 ASYMPTOTIC BEHAVIOR OF CAPACITY OF A SYSTEM OF CLOSELY PLACED BODIES. TAMM SHIELDING. NETWORK APPROXIMATION 57
3.1 Problem of capacity of a system of bodies
57
3.1.1 Tamm shielding effect
58
3.1.2 Two-scale geometry of the problem
59
3.1.3 The physical phenomena determining the asymptotic behavior of capacity of a system of bodies
59
3.2 Formulation of the problem and definitions
61
3.2.1. Formulation of the problem
61
3.2.2 Primal and dual problems and ordinary two-sided estimates
65
3.2.3 The topology of a set of bodies, Voronoi–Delaunay method
68
3.3 Heuristic network model
70
3.4 Proof of the principle theorems
73
3.4.1 Principles of maximum for potentials of nodes in network model
73
3.4.2 Electrostatic channel and trial function
77
3.4.3 Refined lower-bound estimate
78
3.4.4 Refined upper-sided estimate
86
3.5 Completion of proof of the theorems
90
3.5.1 Theorem about NL zones
92
3.5.2 Theorem about asymptotic equivalence of the capacities
96
3.5.3 Theorem about network approximation
98
3.5.4 Asymptotic behavior of capacity of a network
103
3.5.5 Asymptotic of the total flux through network
104
3.6 Some consequences of the theorems about NL zones and network approximation
106
3.6.1 Dykhne experiment and energy localization
106
3.6.2 Explanation of Tamm shielding effect
107
3.7 Capacity of a pair of bodies dependent on shape
108
3.7.1 Capacity of the pair cone–plane
110
3.7.2 Capacity of the pair angle–line
112
3.7.3 Other examples
113
3.7.4 Transport properties of systems of smooth and angular bodies
118
4 NETWORK APPROXIMATION FOR POTENTIALS OF CLOSELY PLACED BODIES 121
4.1 Formulation of the problem of approximation of potentials of bodies
122
4.2 Proof of the network approximation theorem for potentials
125
4.2.1 An auxiliary boundary-value problem
125
4.2.2 An auxiliary estimate for the energies
129
4.2.3 Estimate of difference of solutions of the original problem and the auxiliary problem
132
4.3 The speed of convergence of potentials for a system of circular disks
136
5 ANALYSIS OF TRANSPORT PROPERTIES OF HIGHLY FILLED CONTRAST COMPOSITES USING THE NETWORK APPROXIMATION METHOD 139
5.1 Modification of the network approximation method as applied to particle-filled composite materials
139
5.1.1 Formulation of the problem
140
5.1.2 Effective conductivity of the composite material
143
5.1.3 Modeling particle-filled composite materials using the Delaunay- Voronoi method. The notion of pseudo-particles
146
5.1.4 Heuristic network model for highly filled composite material
147
5.1.5 Formulation of the principle theorems
150
5.2 Numerical analysis of transport properties of highly filled disordered composite material with network model
152
5.2.1 Basic ideas of computation of transport properties of highly filled disordered composite material with network model
153
5.2.2 Numerical simulation for monodisperse composite materials. The percolation phenomenon
156
5.2.3 Numerical results for monodisperse composite materials
157
5.2.4 The polydisperse highly filled composite material
161
6 EFFECTIVE TUNABILITY OF HIGH-CONTRAST COMPOSITES 167
6.1 Nonlinear characteristics of composite materials
167
6.2 Homogenization procedure for nonlinear electrostatic problem
170
6.2.1 Bounds on the effective tunability of a high-contrast composite
183
6.2.2 Numerical computations of homogenized characteristics
185
6.2.3 Note on the decoupled approximation approach
186
6.3 Tunability of laminated composite
187
6.3.1 Tunability of laminated composite in terms of electric displacement
190
6.3.2 Analysis of possible values of effective tunability using convex combinations technique
191
6.3.3 Two-component laminated composite
193
6.4 Tunability amplification factor of composite
194
6.5 Numerical design of composites possessing high tunability amplification factor
196
6.5.1 Ferroelectric–dielectric composite materials
197
6.5.2 Isotropic composite materials
202
6.5.3 Ferroelectric–ferroelectric composite material
203
6.6 The problem of maximum value for the homogenized tunability amplification factor
204
6.7 What determines the effective characteristics of composites?
206
6.8 The difference between design problems of tunable composites in the cases of weak and strong fields
208
6.9 Numerical analysis of tunability of composite in strong fields
211
6.9.1 Numerical method for analysis of the problem
211
6.9.2 Numerical analysis of effective tunability
215
7 EFFECTIVE LOSS OF HIGH-CONTRAST COMPOSITES 219
7.1 Effective loss of particle-filled composite
219
7.1.1 Two-sided bounds on the effective loss tangent of composite material
219
7.1.2 Effective loss tangent of high-contrast composites
220
7.2 Effective loss of laminated composite material
222
8 TRANSPORT AND ELASTIC PROPERTIES OF THIN LAYERS 225
8.1 Asymptotic of first boundary-value problem for elliptic equation in a region with a thin cover
226
8.1.1 Formulation of the problem
226
8.1.2 Estimates for solution of the problem (8.2)–(8.4)
228
8.1.3 Construction of special trial function
233
8.1.4 The convergence theorem and the limit problem
235
8.1.5 Transport property of thin laminated cover
242
8.1.6 Numerical analysis of transport in a body with thin cover
245
8.2 Elastic bodies with thin underbodies layer (glued bodies)
247
8.2.1 Formulation of the problem
248
8.2.2 Estimates for solution of the problem (8.66)
250
8.2.3 Construction of special trial function
259
8.2.4 The convergence theorem and the limit model
259
8.2.5 Stiffness of adhesive joint in dependence on Poisson's ratio of glue
265
8.2.6 Adhesive joints of variable thickness or curvilinear joints
270
APPENDIX A MATHEMATICAL NOTIONS USED IN THE ANALYSIS OF INHOMOGENEOUS MEDIA 273
APPENDIX B DESIGN OF LAMINATED MATERIALS AND CONVEX COMBINATIONS PROBLEM 283
REFERENCES 289
SUBJECT INDEX 317
AUTHOR INDEX 321
A.A. Kolpakov works in the Department of Mathematics and Mechanics at Novosibirsk State University, Russia and Université de Fribourg, Fribourg Pérolles, Switzerland. A.G. Kolpakov works as Marie Curie Fellow at Università degli Studi di Cassino, Italy and Siberian State University of Telecommunications and Informatics, Russia.