Advances in doublet mechanics

Lecture Notes in Physics: Monographs 45 ......Page 1
Advances in Doublet Mechanics ......Page 3
Preface ......Page 7
Table of Contents ......Page 9
List of Figures ......Page 13
1.1 Basic Concepts and Domains of Application ......Page 17
1.1.2 Interpretation ......Page 20
1.1.4 Equilibrium ......Page 22
1.2.1 A Lesson Learned from Elastostatics ......Page 23
1.2.2 Viscoelasticity ......Page 24
1.2.3 Failure Analysis ......Page 25
1.3 Overview of Contents ......Page 27
1.4.1 Kinematics ......Page 30
1.4.2 Microstresses, Equations of Motion, Boundary Conditions ......Page 37
1.4.3 Transition from Microstresses to Macrostresses ......Page 39
1.4.4 Alternative Formulation ......Page 41
2.1 Introduction ......Page 43
2.2 Balance Laws ......Page 44
2.3 Elastic Constitutive Assumptions ......Page 46
2.4 Superposed Rigid Body Motions ......Page 50
2.4.1 Microstrains ......Page 51
2.4.3 Other Functions ......Page 52
2.5 Linear Elastic Doublet Mechanics ......Page 53
2.6 Closure ......Page 54
3.1 Introduction ......Page 57
3.2 Mass Balance ......Page 58
3.3 Dynamic Equations of Motion ......Page 59
3.4 Energy Balance ......Page 60
3.5 Elastic Constitutive Assumptions ......Page 62
3.6 Linearization and Superposed Rigid Body Motions ......Page 63
3.7 Linear Elastic Doublet Mechanics ......Page 64
3.8 Closure ......Page 65
4.2.1 General Remarks ......Page 67
4.2.2 Salient Features ......Page 68
4.2.3 Domains of Inapplicability ......Page 70
4.3.1 Salient Features ......Page 71
4.3.2 Comparison with Classical and Cosserat\'s Theories of Elasticity ......Page 74
4.4.1 Classification ......Page 75
4.4.2 Nonlocal Theories of Differential Type ......Page 76
4.4.3 Nonlocal Theories of Integral Type ......Page 83
4.5.1 Advantages ......Page 88
4.5.2 Domains of Efficient Applicability ......Page 89
4.5.3 Real Solids, Physical Models and Microstructural Parameters ......Page 91
5.1 Introduction ......Page 99
5.2 Dynamic Scaling Equations ......Page 100
5.3 Plane Elastic Waves in Granular Media ......Page 104
5.4 Discussion and Closure ......Page 113
6.1 Introduction ......Page 119
6.2 Model and Formulation of Reflection of Incident Waves ......Page 120
6.3.1 Doublet Axis Parallel to the Reflecting Surface ......Page 123
6.3.2 Doublet Axis at an Angle 7 with Respect to the Reflecting Surface ......Page 125
6.4 Reflection of an Incident P-Wave: Scale Analysis ......Page 127
6.5 Reflection of an Incident S-Wave: Scale Analysis ......Page 132
6.6 Closure ......Page 137
7.1 Introduction ......Page 139
7.2 Geometry, Kinematics and Microstrains ......Page 141
7.4 Difference Kinematic and Constitutive Equations ......Page 145
7.5 Difference Equations of Motion ......Page 149
7.6 Difference Governing Equations ......Page 150
7.7 Continuum Approximation ......Page 151
7.8 Steady-State Waves - General Solution ......Page 155
7.9 Steady-State P- and S-Waves ......Page 161
7.10 Steady-State Surface Wave ......Page 162
7.11 Discussion ......Page 166
7.12 Closure ......Page 170
8.2 Uniqueness Theorem ......Page 173
8.3 Inversion Technique ......Page 175
8.3.1 Homogeneous Deformations ......Page 178
8.3.2 Flamant Problem ......Page 181
8.3.3 Kelvin\'s Problem ......Page 186
8.3.4 Stress Concentration ......Page 187
8.4 Micro-stress Function ......Page 188
8.4.1 Third-Order Polynomial ^-Functions ......Page 189
8.4.2 Flamant\'s Problem ......Page 190
8.5 Closure ......Page 191
9.1 Introduction ......Page 193
9.2 Field Equations and Boundary Conditions ......Page 194
9.3 Aspects of Well-Posedness of the Field Equations ......Page 197
9.4 Kelvin\'s Problem in the Plane ......Page 199
9.5 Discussion ......Page 203
10.2 Discovery ......Page 205
10.3 Theory ......Page 208
10.4 Mechanical Behavior ......Page 209
10.5 Applications ......Page 211
References ......Page 215
A. Micro-macromoduli Relations (K. Mon) ......Page 227