Fundamentals of Continuum Mechanics of Soils

1 Introduction.- 2 Deformation and Strain.- 3 Kinematics.- 4 Balance Equations for Homogeneous Media.- 5 Energetics.- 6 Multi-phase Mixtures.- 7 Constitutive Equations.- 8 The Soil.- 9 Soil as a Multi-phase Mixture.- 10 Flow in Soils.- 11 Volumetrie Stress-Strain Phenomena.- 12 Shear Stress-Strain Phenomena.- 13 Failure.- Appendix A Tensor Mathematics.- A.1 Introduction.- A.2 The Indicial Notation.- A.3 Transformation of Coordinates.- A.4 The Summation Convention.- A.5 The Kronecker Delta.- A.6 Contravariant and Covariant Tensors.- A.7 Symmetric and Skew-symmetric Tensors.- A.8 Addition, Subtraction and Multiplication.- A.9 Contraction.- A.10 The Line Element.- A.11 The Angle between Vectors.- A.12 Lowering and Raising Indices.- A.13 The Christoffel Symbols.- A.14 Covariant Differentiation of Tensors.- A.15 Principal Directions of Second-order Tensors.- A.16 Differential Operators.- A.17 Orthogonal and Cartesian Coordinates.- A.18 Invariants.- A.19 Integrals of Tensor Fields.- A.20 Geometrical Representation of Second-order Tensors.- A.21 Axially Symmetric Second-order Tensors.- Appendix B Cylindrical Coordinates.- B.1 Introduction.- B.2 Definition of the Cylindrical Coordinate System.- B.3 The Fundamental Tensor.- B.4 The Christoffel Symbols.- B.5 Covariant Derivatives.- B.6 Basic Operations of First-order Tensors in Cylindrical Coordinates.- B.7 Elements of Differential Geometry.- B.8 Equations of Kinematics.- B.9 The Strain Tensor.- B.10 The Balance Equations.- Appendix C Rheological Modeling.- C.l Introduction.- C.2 The Hookean Elastic Element.- C.3 The Newtonian Viscous Element.- C.4 Coupling of Rheological Elements.- C.5 St Venant’s Element of Plastic Restraint.- C.6 The Prandtl Body.- C.7 The Maxwell Body.- C.8 The Kelvin Body.- C.9 The Burgers Body.- C.10 The Relations Between Excitation and Response.- C.11 The Relaxation and Creep Functions.- C.12 The General Rheological Models.- C.13 Elastic and Dissipative Excitations.- C.14 The Plastic Restraint.- References.