iMechanica - New Book: Fundamentals of Micromechanics of Solids, by Jianmin Qu and Mohammed Cherkaoui - Comments

Solutions to problems in the new book

Jim S. Olsen — Thu, 01 Nov 2007 14:04:11 -0400

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

Modelling of RVE in ABAQUS

mafarooqi — Mon, 18 Jun 2007 00:42:03 -0400

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

Days when we worked on interfacial fracture mechanics

Zhigang Suo — Sat, 18 Nov 2006 15:25:33 -0500

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.

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

Jianmin Qu — Sat, 18 Nov 2006 14:27:59 -0500

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