Preface ....................................................... vii
1 INTRODUCTION ................................................. 1
2 VOLUME FRACTION CONCEPT ...................................... 5
3 KINEMATICS ................................................... 7
3.1 Вasic Relations ......................................... 7
3.2 Kinematics of Micropolar Constituents .................. 17
4 BALANCE PRINCIPLES .......................................... 21
4.1 Balance of Mass ........................................ 21
4.2 Balance of Momentum and Moment of Momentum ............. 23
4.3 Вalance of Energy ...................................... 26
5 BASIC INEQUALITY (ENTROPY PRINCIPLE) ........................ 29
5.1 Preliminaries .......................................... 29
5.2 Basic Inequality for Non-Polar Constituents and the
Mixture Body ........................................... 30
6 CONSTITUTIVE THEORY ......................................... 33
6.1 Preliminaries .......................................... 33
6.2 Closure Problem and Constraints ........................ 34
6.3 Reformulation of the Entropy Inequality ................ 37
6.4 Exploitation of the Inequality for Ternary and Binary
Capillary Porous Models ................................ 39
6.5 Elastic Behavior of the Solid Skeleton ................. 54
a) Finite Theories ..................................... 54
b) Linear Theory ....................................... 55
c) Other Approaches .................................... 58
6.6 Elastic-Plastic Behavior of the Solid Skeleton ......... 61
a) General Theory ...................................... 61
b) Special Stress-Strain Relations ..................... 73
6.7 Viscous Behavior of the Solid Skeleton ................. 76
6.8 Thermomechanical Behavior of Porefluids ................ 78
a) Inviscid Porefluids ................................. 78
b) Viscous Porefluids .................................. 79
7 FUNDAMENTAL EFFECTS IN GAS - AND LIQUID - FILLED POROUS
SOLIDS ...................................................... 81
7.1 Introduction ........................................... 81
7.2 Basic Equations ........................................ 82
7.3 Uplift ................................................. 83
7.4 Friction ............................................... 86
7.5 Capillarity ............................................ 87
a) Basic Relations ..................................... 88
b) One-Dimensional Capillary Motion .................... 90
c) Two-Dimensional Capillary Motion (an Example) ....... 94
7.6 Effective Stresses ..................................... 95
7.7 Phase Transitions ...................................... 97
a) Theoretical Foundation .............................. 97
b) Drying Processes .................................... 98
c) Freezing Processes ................................. 102
8 POROELASTICITY ............................................. 107
8.1 Introduction .......................................... 107
8.2 The Fundamental Field Equations of Poroelasticity ..... 112
8.3 Main Equations for an Incompressible Binary Model ..... 115
8.4 Basic Solutions for an Incompressible Binary Model .... 118
a) Fundamental Solution of the System of Equations
of Steady Oscillations in the Theory of
Fluidsaturated Porous Media ........................ 118
b) On the Representations of Solutions in the Theory
of Fluidsaturated Porous Media ..................... 126
8.5 Wave Propagation ...................................... 138
a) Plane Waves in a Semi-Infinite Liquidsaturated
Porous Medium ...................................... 139
b) Propagation of Acceleration Waves in S aturated
Porous Solids ...................................... 161
c) Growth and Decay of Acceleration Waves ............. 167
d) Dispersion and Attenuation of Surface Waves in a
Saturated Porous Medium ............................ 176
e) Inhomogeneous Plane Waves, Mechanical Energy
Flux, and Energy Dissipation in a Two-Phase
Porous Medium ...................................... 187
f) Propagation and Evolution of Wave Fronts in
Saturated Porous Solids ............................ 199
9 POROPLASTICITY FOR METALLIC POROUS SOLIDS .................. 205
9.1 Stress-Strain Relations ............................... 206
a) Rigid Ideal-Plastic Behavior ....................... 206
b) Elastic-Plastic Behavior with Hardening ............ 207
9.2 General Theorems for Saturated Porous Solids in the
Rigid Ideal-Plastic Range ............................. 212
a) Preliminaries ...................................... 212
b) The Uniqueness Theorem for Solutions of Boundary
Value Problems ..................................... 218
c) Minimum and Maximum Principles for Rigid
Ideal-Plastic Behavior ............................. 221
10 APPLICATIONS IN ENGINEERING AND BIOMECHANICS ............... 227
10.1 Soil Mechanics ........................................ 227
a) Consolidation Problem and Localization Phenomena ... 227
b) Phase Transitions .................................. 230
c) Dynamics ........................................... 231
10.2 Chemical Engineering .................................. 232
a) Powder Compaction .................................. 232
b) Drying Processes ................................... 234
10.3 Building Physics ...................................... 236
a) Transport of Moisture .............................. 237
b) Heat Conduction in a Fluidsaturated
Capillary-Porous Solid ............................. 241
10.4 Biomechanics .......................................... 245
10.5 Some Other Fields of Application ...................... 248
11 CONCLUSIONS AND OUTLOOK .................................... 251
References .................................................... 253
Author Index .................................................. 273
Subject Index ................................................. 277
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