micromechanicsoverall properties of heterogeneous materials

Microcracks
129
6.4. EFFECTIVE MODULI OF AN ELASTIC SOLID CONTAINING
RANDOMLY DISTRIBUTED SLIT MICROCRACKS
131
6.4.1. Effective Moduli: Random Dilute Distribution of Open
58
2.7. NONMECHANICAL PROPERTIES
ຫໍສະໝຸດ Baidu
59
2.7.1. Averaging Theorems
59
2.7.2. Macropotentials
60
2.7.3. Basic Inequalities
61
2.8. COUPLED MECHANICAL AND NONMECHANICAL PROPERTIES 63
ALIGNED SLIT MICROCRACKS
124
6.3.1. Crack Opening Displacements
125
6.3.2. Effective Moduli: Dilute Distribution of Aligned Microcracks 125
6.3.3. Effective Moduli: Dilute Distribution of Aligned Frictional
6.6.3. Effective Moduli: Self-Consistent Estimates
158
Xll
TABLE OF CONTENTS
6.7. EFFECTIVE MODULI OF AN ELASTIC BODY CONTAINING
PENNY-SHAPED MICROCRACKS PARALLEL TO AN AXIS
Microcracks
131
6.4.2. Effective Moduli: Self-Consistent Estimate
135
6.4.3. Effective Moduli in Antiplane Shear: Random Dilute
Distribution of Frictionless Microcracks
FUNCTION
86
3.2.1. Reciprocal Theorem
87
3.2.2. Superposition
87
3.2.3. Green's Function
88
3.3. REFERENCES
91
SECTION 4. ELASTIC SOLIDS WITH TRACTION-FREE DEFECTS 93
Second Revised Edition
1999 ELSEVIER
Amsterdam - Lausanne - New York - Oxford - Shannon - Singapore - Tokyo
TABLE OF CONTENTS
PREFACE
v
TABLE OF CONTENTS
ix
75
3.1.1. Elastic Moduli
75
3.1.2. Elastic Compliances
77
3.1.3. Elastic Symmetry
78
3.1.4. Plane Strain/Plane Stress
82
3.2. RECIPROCAL THEOREM, SUPERPOSITION, AND GREEN'S
29
2.3. AVERAGE RATE OF STRESS-WORK
31
2.3.1. Uniform Boundary Tractions
33
2.3.2. Linear Boundary Velocities
34
2.3.3. Other Useful Identities
34
2.3.4. Virtual Work Principle
2.8.1. Field Equations
63
2.8.2. Averaging Theorems
65
2.8.3. Stress/Electric-field Potential
66
2.8.4. Strain/Electric-displacement Potential
67
2.8.5. Basic Inequalities
68
2.9. REFERENCES
71
CHAPTER II ELASTIC SOLIDS WITH MICROCAVITIES AND MICROCRACKS 73
SECTION 3. LINEARLY ELASTIC SOLIDS
75
3.1. HOOKE' S LAW AND MATERIAL SYMMETRY
CIRCULAR HOLES
103
5.1.1. Estimates of Three-Dimensional Moduli from Two-Dimensional
Results
104
5.1.2. Effective Moduli: Dilute Distribution of Cavities
106
184
6.9.5. Model Calculations: Faulting
PARTI
OVERALL PROPERTIES OF HETEROGENEOUS MATERIALS
PRECIS: PART 1
CHAPTER I AGGREGATE PROPERTIES
AND AVERAGING METHODS
9
SECTION 1. AGGREGATE PROPERTIES
11
1.1. REPRESENTATIVE VOLUME ELEMENT (RVE)
137
6.4.4. Plane Stress, Plane Strain, and Three-Dimensional Overall
Moduli
140
6.4.5. Effect of Friction and Load-Induced Anisotropy
141
6.5. EFFECTIVE MODULI OF AN ELASTIC BODY CONTAINING
42
2.5.4. On Definition of RVE
44
2.5.5. Linear Versus Nonlinear Response
45
2.5.6. General Relations Between Macropotentials
45
2.5.7. Bounds on Macropotential Functions
micromechanics: overall properties of heterogeneous materials
Sia Nemat-Nasser Department of Applied Mechanics and Engineering Sciences University of California, San Diego La Jolla, CA 6 92093-0416, USA Muneo Hori Earthquake Research Institute University of Tokyo Tokyo, Japan
6.1. OVERALL STRAIN DUE TO MICROCRACKS
121
6.2. OVERALL COMPLIANCE AND MODULUS TENSORS OF HOMO-
GENEOUS LINEARLY ELASTIC SOLIDS WITH MICROCRACKS 123
6.3. EFFECTIVE MODULI OF AN ELASTIC SOLID CONTAINING
ALIGNED PENNY-SHAPED MICROCRACKS
147
6.5.1. Crack-Opening-Displacements
147
6.5.2. Effective Moduli: Dilute Distribution of Aligned Microcracks 147
6.6. EFFECTIVE MODULI OF AN ELASTIC BODY CONTAINING
6.9. BRITTLE FAILURE IN COMPRESSION
174
6.9.1. Introductory Comments
174
6.9.2. Bridgman Paradoxes
176
6.9.3. A New Look at Microcracking in Compression
180
6.9.4. Model Calculations: Axial Splitting
35
2.4. INTERFACES AND DISCONTINUITIES
35
2.5. POTENTIAL FUNCTION FOR MACRO-ELEMENTS
38
2.5.1. Stress Potential
40
2.5.2. Strain Potential
41
2.5.3. Relation between Macropotentials
11
1.2. SCOPE OF THE BOOK
16
1.3. DESCRIPTION OF RVE
19
1.4. REFERENCES
23
SECTION 2. AVERAGING METHODS
27
2.1. AVERAGE STRESS AND STRESS RATE
27
2.2. AVERAGE STRAIN AND STRAIN RATE
98
4.5. OVERALL ELASTICITY TENSOR FOR POROUS ELASTIC
SOLIDS
100
4.6. REFERENCES
102
TABLE OF CONTENTS
XI
SECTION 5. ELASTIC SOLIDS WITH MICROCAVITIES
103
5.1. EFFECTIVE MODULI OF AN ELASTIC PLATE CONTAINING
162
6.8. INTERACTION EFFECTS
167
6.8.1. Crack-Opening-Displacements and Associated Strains
168
6.8.2. Dilute Distribution of Parallel Crack Arrays
170
6.8.3. Randomly Oriented Open Slit Crack Arrays Parallel to an Axis 172
5.1.3. Effective Moduli: Self-Consistent Estimates
111
5.1.4. Effective Moduli in x3-Direction
113
5.2. EFFECTIVE BULK MODULUS OF AN ELASTIC BODY
CONTAINING SPHERICAL CAVITIES
50
TABLE OF CONTENTS
2.6. STATISTICAL HOMOGENEITY, AVERAGE QUANTITIES, AND
OVERALL PROPERTIES
53
2.6.1. Local Average Fields
55
2.6.2. Limiting Process and Limit Fields
115
5.3. ENERGY CONSIDERATION AND SYMMETRY PROPERTIES OF
TENSOR H
117
5.4. CAVITY STRAIN
118
5.5. REFERENCES
119
SECTION 6. ELASTIC SOLIDS WITH MICROCRACKS
121
4.1. STATEMENT OF PROBLEM AND NOTATION
93
4.2. AVERAGE STRAIN FOR PRESCRIBED MACROSTRESS
95
4.3. OVERALL COMPLIANCE TENSOR FOR POROUS ELASTIC
SOLIDS
97
4.4. AVERAGE STRESS FOR PRESCRIBED MACROSTRAIN
RANDOMLY DISTRIBUTED PENNY-SHAPED MICROCRACKS 151
6.6.1. Dilute Open Microcracks with Prescribed Distribution
151
6.6.2. Effective Moduli: Random Dilute Distribution of Microcracks 154