Mechanics and Physics of Structured Media

Asymptotic and Integral Equations Methods of Leonid Filshtinsky.

Igor Andrianov, Simon Gluzman, Vladimir Mityushev

• Publisher: Academic Press
• Year: 2022
• Print ISBN:
  9780323905435
• eBook ISBN:
  9780323906531
• Topic: Technology & Engineering
• Subtopic: Materials Science
• Index: Technology & Engineering

Mechanics and Physics of Structured Media: Asymptotic and Integral Methods of Leonid Filshtinsky provides unique information on the macroscopic properties of various composite materials and the mathematical techniques key to understanding their physical behaviors. The book is centered around the arguably monumental work of Leonid Filshtinsky. His last works provide insight on fracture in electromagnetic-elastic systems alongside approaches for solving problems in mechanics of solid materials. Asymptotic methods, the method of complex potentials, wave mechanics, viscosity of suspensions, conductivity, vibration and buckling of functionally graded plates, and critical phenomena in various random systems are all covered at length. Other sections cover boundary value problems in fracture mechanics, two-phase model methods for heterogeneous nanomaterials, and the propagation of acoustic, electromagnetic, and elastic waves in a one-dimensional periodic two-component material. - Covers key issues around the mechanics of structured media, including modeling techniques, fracture mechanics in various composite materials, the fundamentals of integral equations, wave mechanics, and more - Discusses boundary value problems of materials, techniques for predicting elasticity of composites, and heterogeneous nanomaterials and their statistical description - Includes insights on asymptotic methods, wave mechanics, the mechanics of piezo-materials, and more - Applies homogenization concepts to various physical systems

Table of contents

• Cover Image
• Title Page
• Copyright
• Leonid Anshelovich Filshtinsky
• Table of Contents
• List of contributors
• Acknowledgements
• Chapter 1 L.A. Filshtinsky's contribution to Applied Mathematics and Mechanics of Solids
• Chapter 2 Cracks in two-dimensional magneto-electro-elastic medium
• Chapter 3 Two-dimensional equations of magneto-electro-elasticity
• Chapter 4 Hashin-Shtrikman assemblage of inhomogeneous spheres
• Chapter 5 Inverse conductivity problem for spherical particles
• Chapter 6 Compatibility conditions: number of independent equations and boundary conditions
• Chapter 7 Critical index for conductivity, elasticity, superconductivity. Results and methods
• Chapter 8 Double periodic bianalytic functions
• Chapter 9 The slowdown of group velocity in periodic waveguides
• Chapter 10 Some aspects of wave propagation in a fluid-loaded membrane
• Chapter 11 Parametric vibrations of axially compressed functionally graded sandwich plates with a complex plan form
• Chapter 12 Application of volume integral equations for numerical calculation of local fields and effective properties of elastic composites
• Chapter 13 A slipping zone model for a conducting interface crack in a piezoelectric bimaterial
• Chapter 14 Dependence of effective properties upon regular perturbations
• Chapter 15 Riemann-Hilbert problems with coefficients in compact Lie groups
• Chapter 16 When risks and uncertainties collide: quantum mechanical formulation of mathematical finance for arbitrage markets
• Chapter 17 Thermodynamics and stability of metallic nano-ensembles
• Chapter 18 Comparative analysis of local stresses in unidirectional and cross-reinforced composites
• Chapter 19 Statistical theory of structures with extended defects
• Chapter 20 Effective conductivity of 2D composites and circle packing approximations
• Chapter 21 Asymptotic homogenization approach applied to Cosserat heterogeneous media
• Appendix A Finite clusters in composites
• Index