Skip to main content
Elsevier
View Cart

Mechanics and Physics of Structured Media

Asymptotic and Integral Equations Methods of Leonid Filshtinsky.

  • 1st Edition - January 20, 2022
  • Latest edition
  • Editors: Igor Andrianov, Simon Gluzman, Vladimir Mityushev
  • Language: English

Mechanics and Physics of Structured Media: Asymptotic and Integral Methods of Leonid Filshtinsky provides unique information on the macroscopic properties of various composite ma… Read more

World Book Day celebration

Where learning shapes lives

Up to 25% off trusted resources that support research, study, and discovery.

Explore resources

Description

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.

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

Readership

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
Vladimir Mityushev, Igor Andrianov, and Simon Gluzman

2. Cracks in two-dimensional magneto-electro-elastic medium
D. Nosov, L.A. Filshtinskii, and V. Mityushev

3. Two-dimensional equations of magneto-electro-elasticity
V. Mityushev, D. Nosov, and R. Wojnar

4. Hashin-Shtrikman assemblage of inhomogeneous spheres
A. Cherkaev and V. Mityushev

5. Inverse conductivity problem for spherical particles
Vladimir Mityushev, Natalia Rylko, Zhanat Zhunussova, and Yeskendyr Ashimov

6. Compatibility conditions: number of independent equations and boundary conditions
I.V. Andrianov and H. Topol

7. Critical index for conductivity, elasticity, superconductivity. Results and methods
Simon Gluzman

8. Double periodic bianalytic functions
Piotr Drygas

9. The slowdown of group velocity in periodic waveguides
Yuri A. Godin and Boris Vainberg

10. Some aspects of wave propagation in a fluid-loaded membrane
J. Kaplunov, L. Prikazchikova, and S. Shamsi

11. Parametric vibrations of axially compressed functionally graded sandwich plates with a complex planform
Kurpa Lidiya and Shmatko Tetyana

12. Application of volume integral equations for numerical calculation of local fields and effective properties of
elastic composites
S. Kanaun and A. Markov

13. A slipping zone model for a conducting interface crack in a piezoelectric bimaterial
V. Loboda, A. Sheveleva, and O. Mykhail

14. Dependence of effective properties upon regular perturbations
Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino, and Roman Pukhtaievych

15. Riemann-Hilbert problems with coefficients in compact Lie groups
G. Giorgadze and G. Khimshiashvili

16. When risks and uncertainties collide: quantum mechanical formulation of mathematical finance for
arbitrage markets
Simone Farinelli and Hideyuki Takada

17. Thermodynamics and stability of metallic nano-ensembles
Michael Vigdorowitsch

18. Comparative analysis of local stresses in unidirectional and cross-reinforced composites
A.G. Kolpakov and S.I. Rakin

19. Statistical theory of structures with extended defects
V.I. Yukalov and E.P. Yukalova

20. Effective conductivity of 2D composites and circle packing approximations
Roman Czapla and Wojciech Nawalaniec

21. Asymptotic homogenization approach applied to Cosserat heterogeneous media
Victor Yanes, Federico J. Sabina, Yoanh Espinosa-Almeyda,
Jose A. Otero, and Reinaldo Rodríguez-Ramos

Product details

  • Edition: 1
  • Latest edition
  • Published: January 25, 2022
  • Language: English

About the editors

IA

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

SG

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

VM

Vladimir Mityushev

Vladimir Mityushev is the Professor of Cracow University of Technology, a leader of the research group www.materialica.plus. 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

View book on ScienceDirect

Read Mechanics and Physics of Structured Media on ScienceDirect