Classical Thermodynamics

Short Introduction to Mechanics of Nanocomposites

  • Author: Alexander N.Guz, Jeremiah J. Rushchitsky
  • ISBN: 978-0-9838996-9-3

Professor D.Sc. Alexander N.Guz is serving from 1976 until present as Director of the SP Timoshenko Institute of Mecha-nics, Kyiv, Ukraine. He is Academician of the National Aca-demy of Sciences of Ukraine (1978), Member of the Acade-mia Europaea (1992), Fellow of the New York Academy of Sciences (1997), Fellow of the World Innovation Foundation (2001), Member of the European Academy of Sciences (2002). The principal scientific results are obtained in mechanics of de-formable solids and related problems of continuum mechanics: the three-dimensional theory of stability of deformable bodies; the theory of propagation and diffraction of elastic waves in multi-connected bodies and bodies with initial stresses; stress concentration around holes in shells; mechanics of composites materials and structural members utilizing them; aerohydroelasticity; non-classical problems of fracture mechanics; rock mechanics; dynamics of viscous compressible liquid; contact problems; mechanics of nano-composites and non-destructive methods of stress determination. He is an author or co-author of 61 books (including 15 solo) and about 900 scientific papers (including more than 400 solo). He has trained 35 Doctors of Sciences and about 100 Candidates of Sciences (PhD).

Prof. D.Sc. Jeremiah J. Rushchitsky is Head of the Depart-ment of Rheology at SP Timoshenko Institute of Mecha-nics, Kyiv, Ukraine; Professor at Physical-Mathematical Faculty, National Technical University of Ukraine “KPI”, Kyi. He is an author of 430 publications, including 7 monographs on waves and composite materials and 7 university text-books on waves in materials, viscoelasticity, wavelet and fractal analysis; about 230 journal papers, 6 State Stand- ards and so on. The main scientific results are obtained in mechanics of nano- and micro-composite materials, linear and nonlinear waves in materials with internal structure, multiphase media, viscoelasticity, wavelet analysis as app-lied to wave propagation.

Description

Guz A.N., Rushchitsky J.J. "Short Introduction to Mechanics of Nanocomposites"

The monograph is devoted to a statement of the proposed by authors general approach to constructing the fundamentals of mechanics of nanocomposites, which takes into account the transition from discrete (atomic) structure to continuum mechanics. The concrete results for some classes of problems related to the problems of statics, dynamics and stability of nanocomposites. The essential attention is drawn to constructing the mechanics of nano-composites as the constituent part of structural mechanics of materials. Owing the intro-ductory character and the presentation of the general approach, the monograph can be used as a source of primary information for the wide circle of specialists in related problems of natural science and engineering science, who wish getting to know one of the thriving mo-dern scientific-technical directions. The monograph is oriented on specialists in mechanics of composite materials, nanomaterial science, and mechanics of solids; it will be useful also for lecturers, post-graduate and under-graduate students of corresponding specialities.

Table of Contents

FOREWORD ………1
INTRODUCTION ………6
  I.1. Short-form historical sketch ………6
  I.2. Examples of nanotechnologies and nanomaterials ………8
  I.3. On practicability making the nanocomposites ………16
  I.4. On position of mechanics in nanomaterial science ………16
  I.5. Final remarks ………20
Chapter 1
ON STRUCTURAL MECHANICS OF MATERIALS ………21
  1.1. On mechanics of materials ………21
  1.2. Structural levels ………23
  1.3. On modeling in structural mechanics of materials.
     Principles of continualization and homogenization
………24
  1.4. To edge or near-the-surface effects ………30
  1.5. On validity ranges of continuum mechanics of solids ………34
  1.6. Two basic models in structural mechanics of materials ………36
Chapter 2
ON CLASSIFICATION OF NANOCOMPOSITES ………38
  2.1. Nanocomposites in the form of matrix dispersion-
     stiffened by separate particles of nanoformations
     for small volume fraction of nanoformations
………38
  2.2. Layered nanocomposites ………40
  2.3. Fibrous nanocomposites ………41
  2.4. Granular nanocomposites ………42
  2.5. Complex nanocomposites ………43
Chapter 3
BRIEF INFORMATION ON PROPERTIES
OF NANOFORMATIONS AND NANOCOMPOSITES
………44
  3.1. Description of nanotubes ………44
  3.2. Properties of nanotubes and nanoformations.
     Theoretical and experimental results
………47
  3.3. Properties of a matrix (a binder). On estimation
     of the value of interface area
………50
  3.4. On phenomena at interface in nanocomposites ………53
Chapter 4
SHORT-FORM INFORMATION ON NANOCOMPOSITES
OF COMPLEX STRUCTURE
………55
  4.1. Examples of nanofillers of complex structure ………55
  4.2. Nanofiber in the form of a multilevel nanocomposite ………59
  4.3. Cup-stacked-type of carbon nanofibers ………61
   4.4. To determination of properties of nanofillers ………64
Chapter 5
BASIC APPROACH TO CONSTRUCTING
THE MECHANICS OF NANOCOMPOSITES
………66
  5.1. Basic problems in constructing
     the mechanics of nanocomposites
………66
  5.2. Description of properties of nanofillers ………67
  5.3. Description of properties of matrix (polymeric binder) ………74
   5.4. Determination of averaged properties of nanocomposites
     enabling the transition to mechanics of structural elements
………76
   5.5. Short-form formulation of the basic approach ………76
Chapter 6
ON BILATERAL ESTIMATES
IN MECHANICS OF NANOCOMPOSITES
………77
  6.1. Bilateral estimates in fracture mechanics
     of nanocomposites under compression
………77
  6.2. On bilateral estimates in evaluation
     of averaged constants
………82
  6.3. Bilateral estimates in the linear theory
     of wave propagation
………85
Chapter 7
FIBROUS NANOCOMPOSITES OF COMPLEX STRUCTURE ………90
  7.1. Description of the approach to modeling and the
     structure of a "bristled" ("whiskerized") nanofiber
………90
  7.2. Structural and theoretical schemes of nanocomposite
     reinforced by the "bristled" nanofibers
………94
  7.3. Theoretical multicomponent models.
     Determination of averaged elastic constants
………96
  7.4. Numerical results for concrete materials ………102
Chapter 8
GRANULAR NANOCOMPOSITES OF COMPLEX STRUCTURE ………106
  8.1. Description of the structure of
     a "bristled knedel-like" nanogranule
………106
  8.2. Theoretical schemes of nanocomposite reinforced
     by the "bristled knedel-like" nanogranules
………109
  8.3. Determination of averaged elastic constants ………110
  8.4. Numerical results for concrete materials ………117
Chapter 9
NANOCOMPOSITES WITH NANOTUBES
OF A CURVED SHAPE
………118
  9.1. On description of curvature of fillers ………118
  9.2. Nanocomposites with large-scale curvatures of nanotubes.
     Continuum model
………121
  9.3. Nanocomposites with small-scale curvatures of nanotubes.
     Continuum model
………127
  9.4. Nanocomposites with periodically small-scale curvatures
     of nanotubes. Model of piece-wise homogeneous material
………136
  9.5. Final remarks to chapters 7 - 9 ………147
AFTERWORD ………148
REFERENCES ………150
SUBJECT INDEX ………158