Fundamentals of Continuum Mechanics of Soils

by Yehuda Klausner

Overview

Fundamentals of Continuum Mechanics of Soils provides a long-needed general scheme for the study of the important yet problematic material of soil. It closes the gap between two disciplines, soil mechanics and con- tinuum mechanics, showing that the familiar concepts of soil mechanics evolve directly from continuum mechanics. It confirms concepts such as pore pressures, cohesion and dependence of the shear stress on consolidation, and rejects the view that continuum mechanics cannot be applied to a material such as soil. The general concepts of continuum mechanics, field equations and constitutive equations are discussed. It is shown how the theory of mixtures evolves from these equations and how, along with energetics and irrevers- ible thermodynamics, it can be applied to soils. The discussion also sheds light on some aspects of mechanics of materials, especially compressible materials. Examples are the introduction of the Hencky measure of strain, the requirement of dual constitutive equations, and the dependence of the spent internal energy on the stored internal energy. Researchers in engineering mechanics and material sciences may find that the results of experiments on soils can be generalized and extended to other materials. The book is a reference text for students familiar with the fundamentals of mechanics, for scholars of soil engineering, and for soil scientists. It is also suitable as an advanced undergraduate course in soil mechanics.

Product Details

ISBN-13:	9781447116790
Publisher:	Springer London
Publication date:	11/25/2011
Edition description:	Softcover reprint of the original 1st ed. 1991
Pages:	607
Product dimensions:	6.69(w) x 9.53(h) x 0.05(d)

Table of Contents

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.