Random Heterogeneous Materials

Microstructure and Macroscopic Properties
Softcover Nachdruck of the original 1. Auflage 2002
ISBN: 978-1-4757-6357-7
Verlag: Springer

Buch, Englisch, Band 16, 703 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 1344 g

Reihe: Interdisciplinary Applied Mathematics

The interdisciplinary subject of random heterogeneous materials has experienced remarkable growth since the publication of the well-known monograph Statistical Con­ tinuum Theories by Beran ( 1968). Many of these advances, especially those concerning the statistical characterization of the microstructure and its effect on the physical prop­ erties of the material, have not been treated fully in any book. One of the intents of the present book is to fill this gap. This book also distinguishes itself in that it provides a unified rigorous framework to characterize the microstructures and macroscopic properties of the widely diverse types of heterogeneous materials found in nature and synthetic products. Emphasis is placed on providing foundational theoretical methods that can simultaneously yield results of practical utility. This book treats a wide breadth of topics, but the choice of subjects naturally reflects my own interests. The sheer enormity of the field has prevented me from covering many important topics. I apologize to those colleagues, known and unknown, who may not find enough of their own work cited in the ensuing pages.

Zielgruppe

Research

Autoren/Hrsg.

Torquato, Salvatore

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Werkstoffprüfung
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Mathematik | Informatik Mathematik Stochastik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie

Inhaltsverzeichnis

1 Motivation and Overview.- 2 Microstructural Descriptors.- 3 Statistical Mechanics of Many-Particle Systems.- 4 Unified Approach to Characterize Microstructure.- 5 Monodisperse Spheres.- 6 Polydisperse Spheres.- 7 Anisotropic Media.- 8 Cell and Random-Field Models.- 9 Percolation and Clustering.- 10 Some Continuum Percolation Results.- 11 Local Volume Fraction Fluctuations.- 12 Computer Simulations, Image Analyses, and Reconstructions.- 13 Local and Homogenized Equations.- 14 Variational Principles.- 15 Phase-Interchange Relations.- 16 Exact Results.- 17 Single-Inclusion Solutions.- 18 Effective-Medium Approximations.- 19 Cluster Expansions.- 20 Exact Contrast Expansions.- 21 Rigorous Bounds.- 22 Evaluation of Bounds.- 23 Cross-Property Relations.- A Equilibrium Hard-Disk Program.- B Interrelations Among Two- and Three-Dimensional Moduli.- References.