Fundamentals of Micromechanics of Solids

Preface

1 Introduction

1.1 Background and Motivation

1.2 Objectives

1.3 Organization of Book

1.4 Notation Conventions

References

2 Basic Equations of Continuum Mechanics

2.1 Displacement and Deformation

2.2 Stresses and Equilibrium

2.3 Energy, Work, and Thermodynamic Potentials

2.4 Constitutive Laws

2.5 Boundary Value Problems for Small-Strain Linear Elasticity

2.6 Integral Representations of Elasticity Solutions

Problems

Appendix 2.A

Appendix 2.B

Appendix 2.C

References

Suggested Readings

3 Eigenstrains

3.1 Definition of Eigenstrains

3.2 Some Examples of Eigenstrains

3.3 General Solutions of Eigenstrain Problems

3.4 Examples

Problems

Appendix 3.A

Appendix 3.B

References

Suggested Readings

4 Inclusions and Inhomogeneities

4.1 Definitions of Inclusions and Inhomogeneities

4.2 Interface Conditions

4.3 Ellipsoidal Inclusion with Uniform Eigenstrains (Eshelby Solution)

4.4 Ellipsoidal Inhomogeneities

4.5 Inhomogeneous Inhomogeneities

Problems

Appendix 4.A

Appendix 4.B

Suggested Readings

5 Definitions of Effective Moduli of Heterogeneous Materials

5.1 Heterogeneity and Length Scales

5.2 Representative Volume Element

5.3 Random Media

5.4 Macroscopic Averages

5.5 Hill's Lemma

5.6 Definitions of Effective Modulus of Heterogeneous Media

5.7 Concentration Tensors and Effective Properties

Problems

Suggested Readings

6 Bounds for Effective Moduli

6.1 Classical Variational Theorems in Linear Elasticity

6.2 Voigt Upper Bound and Reuss Lower Bound

6.3 Extensions of Classical Variational Principles

6.4 Hashin-Shtrikman Bounds

Problems

Appendix 6.A

References

Suggested Readings

7 Determination of Effective Moduli

7.1 Basic Ideas of Micromechanics for Effective Properties

7.2 Eshelby Method

7.3 Mori-Tanaka Method

7.4 Self-Consistent Methods for Composite Materials

7.5 Self-Consistent Methods for

Jianmin Qu is a professor in the G. W. Woodruff School of Mechanical Engineering at Georgia Institute of Technology in Atlanta.

Mohammed Cherkaoui, Phd, is a professor in the G. W. Woodruff School of Mechanical Engineering at Georgia Institute of Technology in Atlanta. He is formerly with the Université de Metz, France.