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Mechanics and Physics of Structured Media - 1st Edition - ISBN: 9780323905435

Mechanics and Physics of Structured Media

1st Edition

Asymptotic and Integral Equations Methods of Leonid Filshtinsky.

Editors: Igor Andrianov Simon Gluzman Vladimir Mityushev
Paperback ISBN: 9780323905435
Imprint: Academic Press
Published Date: 1st January 2022
Page Count: 500
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Mechanics and Physics of Structured Media: Symptotic and Integral Methods of Leonid Filshtinsky provides critical information on the macroscopic properties of various composite materials and the mathematical functions and equations key to understanding their mechanical behaviors. Centered around, and building upon, the monumental work of Leonid Filshtinsky, the book provides insights 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, sedimentation velocity, 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, short-time and non-local diffusion, and the propagation of acoustic, electromagnetic, and elastic waves in a one-dimensional periodic two-component material.

Key Features

  • 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


Researchers, graduate students, and professional engineers/R&D professionals in mechanical engineering, material science, physics

Table of Contents

  1. L.A. Filshtinsky's contribution to Applied Mathematics and Mechanics of Solids
    2. Cracks in two-dimensional magneto-electro-elastic medium
    3. Two-dimensional equations of magneto-electro-elasticity
    4. Hashin-Shtrikman assemblage of inhomogeneous spheres
    5. Inverse problem for highly conducting spherical particles
    6. Compatibility conditions: number of independent equations and boundary conditions
    7. Critical Index for Conductivity, Elasticity, Superconductivity. Results and Methods
    8. Double periodic bianalytic functions
    9. Slowdown of group velocity in periodic waveguides
    10. Some aspects of wave propagation in a fluid-loaded membrane
    11. Parametric vibrations of axially compressed functionally graded sandwich plates with a complex planform
    12. Homogenization method based on integral equations for heterogeneous media. Choice of representative volume element
    13. A Slipping Zone Model for Conducting an Interface Crack in a Piezoelectric Bimaterial
    14. Dependence of effective properties upon regular perturbations
    15. Riemann-Hilbert problems with coefficients in compact Lie groups
    16. Finance as Mechanics. Quantum Mechanical Formulation of Mathematical Finance for Arbitrage Markets
    17. Thermodynamics and stability of metallic Nano-ensembles
    18. Comparative analysis of local stresses in unidirectional and cross-reinforced composites
    19. Statistical theory of structures with extended defects
    20. Effective conductivity of 2D composites and circle packing approximations


No. of pages:
© Academic Press 2022
1st January 2022
Academic Press
Paperback ISBN:

About the Editors

Igor Andrianov

Igor V. Andrianov is Professor Emeritus, RWTH Aachen University. He is the author or co-author of 14 books and more than 300 papers in peer-reviewed journals. He has presented papers at more than 150 international conferences and seminars and also supervised 21 PhD. Students. His research interests include mechanics of solids, mechanics of composite materials, nonlinear dynamics, and asymptotic methods.

Affiliations and Expertise

Professor Emeritus, RWTH Aachen University, Germany

Simon Gluzman

Simon Gluzman is presently an Independent Researcher (Toronto, Canada) and formerly a Research Associate at PSU in Applied Mathematics. He is interested in Re-summation methods in theory of random and regular composites and the method of self-similar and rational approximants.

Affiliations and Expertise

Independent Researcher, Toronto, Canada

Vladimir Mityushev

Vladimir Mityushev is the Professor of Cracow University of Technology, a leader of the research group He is interested in mathematical modeling and computer simulations, Industrial mathematics and boundary value problems and their applications. .

Affiliations and Expertise

Institute of Mathematics, Faculty of Computer Science and Telecommunications, Cracow University of Technology, Kraków, Poland

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