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# New Book: Fundamentals of Micromechanics of Solids, by Jianmin Qu and Mohammed Cherkaoui

Fundamentals of Micromechanics of Solids, Jianmin Qu, Mohammed Cherkaoui

ISBN: 0-471-46451-1, Hardcover, 400 pages, August 2006, US $120.00

PART I: LINEAR MICROMECHANICS AND BASIC CONCEPTS

**Chapter 1 INTRODUCTION**

- 1.1 Background and Motivation
- 1.2 Objectives
- 1.3 Organization of Book
- 1.4 Notation Conventions
- References

**Chapter 2 BASIC EQUATIONS OF CONTINUUM MECHANICS **

- 2.1 Displacement and Deformation
- 2.2 Stresses and Equilibrium
- 2.3 Energy, Work, and Thermodynamics Potentials
- 2.4 Constitutive Laws
- 2.5 Boundary Value Problems for Small-Strain Linear Elasticity
- 2.6 Integral Representations of the Elasticity Solutions
- Problems
- Appendix 2.A
- Appendix 2.B
- Appendix 2.C
- References and Suggested Readings

**Chapter 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 and Suggested Readings

**Chapter 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
- References and Suggested Readings

**Chapter 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
- References and Suggested Readings

**Chapter 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
- References and Suggested Readings
- Appendix 6.A

**Chapter 7 DETERMINATION OF EFFECTIVE MODULI**

- 7.1 Basic Ideas of Micromechanics for Effective Properties
- 7.2 The Eshelby Method
- 7.3 The Mori-Tanaka Method
- 7.4 Self-Consistent Methods for Composite Materials
- 7.5 Self-Consistent Methods for Polycrystalline Materials
- 7.6 Differential Schemes
- 7.7 Comparison of Different Methods
- Problems
- References and Suggested Readings

**Chapter 8 DETERMINATION OF THE EFFECTIVE MODULI- MULTI-INCLUSION APPROACHES**

- 8.1 The Composite-Sphere Model
- 8.2 The Three-Phase model§8.3 The Four-Phase Model
- 8.4 The Multicoated Inclusion Problem
- Problems
- Appendix 8.A
- Appendix 8.B
- Appendix 8.C
- References and Suggested Readings

**Chapter 9 EFFECTIVE PROPERTIES OF FIBER-REINFORCED COMPOSITE LAMINATES**

- 9.1 Unidirectional Fiber-Reinforced Composites
- 9.2 Effective Properties of Multilayer Composites
- 9.3 Effective Properties of a Lamina
- 9.4 Effective Properties of a Laminated Composite Plate
- Problems
- Appendix 9.A
- References and Suggested Readings

**Chapter 10 BRITTLE DAMAGE AND FAILURE OF ENGINEERING COMPOSITES**

- 10.1 Imperfect Interfaces
- 10.2 Fiber Bridging
- 10.3 Transverse Matrix Cracks
- Problems
- Appendix 10.A
- References and Suggested Readings

**Chapter 11 MEAN FIELD THEORY FOR NONLINEAR BEHAVIOR**

- 11.1 Eshelby's Solution and Kröner's Model
- 11.2 Applications§11.3 Time-Dependent Behavior of Polycrystalline Materials: Secant Approach
- Problems
- References and Suggested Readings

**Chapter 12 NON LINEAR PROPERTIES OF COMPOSITES MATERIALS - THERMODYNAMIC APPROACHES**

- 12.1 Nonlinear Behavior of Constituents
- 12.2 Effective Potentials
- 12.3 Secant Approach
- Problems
- References and Suggested Readings

**Chapter 13 MICROMECHANICS OF MARTENSITIC TRANSFORMATION IN SOLIDS **

- 13.1 Phase Transformation Mechanisms at Different Scales§13.2. Application: Thermodynamic Forces and Constitutive Equations for Single Crystals
- 13.3. Overall Behavior of Polycrystalline Materials with Phase Transformation
- Problems
- References and Suggested Readings

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## Comments

## Days when we worked on interfacial fracture mechanics

Jianmin: Congratulations on the new book! Thank you so much for posting the news in iMechanica. The new book reminds me of the days when I was a graduate student, studying the papers by you and John Bassani on cracks on an interface between two anisotropic materials.

Your publisher has sent my a copy of the book. It looks excellent. I've asked our library to order a copy of the book, and place it on the reserve list for a course I'm teaching.

## Modelling of RVE in ABAQUS

Hi All,

Could anyone anyone please tell me how to model a periodic representative volume element in ABAQUS. I tried doing it by creating 2 parts, one a rectangular matrix-part with a square or circular hollow space in the center to accomodate and the second one that represents fiber or inclusion. Then defined 2 materials, each for matrix and inclusion. Finally assemble the two part instances in assembly module. Giving appropriate boundary conditions and loads, meshing the assembly and submitted he job. But it gives error messege:

(For heat Transfer problem) No valid output requests have been generated, this may be due to earlier input error or specifications of a non-existant cavity or surface name.The second error messege is: A heat transfer analysis is not meaningful as there is no temperature degrees of freedom in the model.I followed the same procedure to model the same heat transfer problem using a shell element with a single homogeneous material, the analysis runs well and gives nice results.

Please give suggestions.

Thanks

## Solutions to problems in the new book

Dear Professor Qu

I am a rather fresh PhD-student who is working on shape memory alloys. The main focus of my work will be on the effect of inclusions on SMA's properties and behaviour. I have taken no formal courses in micromechanics so I basically need to learn it from scratch by myself. I retrieved your book from my supervisor Prof. Zhiliang Zhang and it seems to be a good introduction to micromechanics, which is what I need. My idea is to thoroughly work trough your book to get a basic understanding of this topic. So my question to you is: Have you made solutions to the problems in teh book? And if you do, is it possible to receive a copy of these? It would be very helpful to me at the present stage of my work.

Best Regards

Jim S.

Olsen

PhD

Student

Faculty of Engineering

Science and Technology

Norwegian University of Science and technology

N-7491

Trondheim

Norway

Tel:

0047-73594884

## Solutions to problems

Anyone has solutions to the problems in the book?, even to some problmes from courses taught by the authors at metz and Gerogia Tech would help!