Heterogeneous Materials I (Interdisciplinary Applied Mathematics Series): Linear Transport and Optical Properties, Vol. 22
This book describes and discusses the properties of heterogeneous materials. The properties considered include the conductivity (thermal, electrical, magnetic), elastic moduli, dielectrical constant, optical properties, mechanical fracture, and electrical and dielectrical breakdown properties. Both linear and nonlinear properties are considered. The nonlinear properties include those with constitutive nonlinearities as well as threshold nonlinearities, such as brittle fracture and dielectric...
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This book describes and discusses the properties of heterogeneous materials. The properties considered include the conductivity (thermal, electrical, magnetic), elastic moduli, dielectrical constant, optical properties, mechanical fracture, and electrical and dielectrical breakdown properties. Both linear and nonlinear properties are considered. The nonlinear properties include those with constitutive non-linearities as well as threshold non-linearities, such as brittle fracture and dielectric breakdown. A main goal of this book is to compare two fundamental approaches to describing and predicting materials properties, namely, the continuum mechanics approach, and those based on the discrete models. The latter models include the lattice models and the atomistic approaches. The book provides comprehensive and up to date theoretical and computer simulation analysis of materials' properties. Typical experimental methods for measuring all of these properties are outlined, and comparison is made between the experimental data and the theoretical predictions. Volume I covers linear properties, while Volume II considers non-linear and fracture and breakdown properties, as well as atomistic modeling. This multidisciplinary book will appeal to applied physicists, materials scientists, chemical and mechanical engineers, chemists, and applied mathematicians.
Introduction\ • Characterization of Connectivity and Clustering\ • Characterization and Modeling of the Morphology\ • Effective Conductivity, Dielectric Constant and Optical Properties: The Continuum Approach\ • Effective Conductivity and Dielectric Constant: The Discrete Approach\ • Frequency-Dependent Properties: The Discrete Approach\ • Rigidity and Elastic Properties: The Continuum Approach\ • Rigidity and Elastic Properties: The Discrete Approach\ • Rigidity and Elastic properties of Network Glasses, Polymers, and Composite Solids: The Discrete Approach\ • References\ • Index
