With the present state of development of finite element computer software and high-speed digital computer hardware, an almost unlimited number of solutions to soil mechanics and soil structure interaction problems can now be obtained. These are not limited to linear elastic small deformation solid mechanics, but can be extended to include problems of various kinds involving material and geometric nonlinearities. This book is concerned with the development of numerical tools for solutions of nonlinear analysis problems in soil mechanics.
Part I. FUNDAMENTALS. 1. Introduction. Characteristics of soil behavior.Idealizations and material modeling. Historical review of plasticity in soil mechanics. Nonlinear stress analyses in geotechnical engineering. Need, objectives and scope. References. 2. Basic Concept of Continuum Mechanics. Introduction. Notations. Stresses in three dimensions. Definitions and notations. Cauchy's formulas, index notation, and summation convention. Principal axes of stresses. Deviatoric stress. Geometrical representation of stresses. Strains in three dimensions. Definitions and notations. Deviatoric strain. Octahedral strains and principal shear strains. Equations of solid mechanics. Equations of equilibrium (or motion). Geometric (compatibility) conditions. Constitutive relations. Summary. References. Part II. MATERIAL MODELING-BASIC CONCEPTS. 3. Elasticity and Modeling . Introduction. Elastic models in geotechnical engineering. Linear elastic model (generalized Hooke's law). Cauchy elastic model. Hyperelastic model. Hypoelastic model. Uniqueness, stability, normality, and convexity for elastic materials. Uniqueness. Drucker's stability postulate. Existence of W and v. Restrictions - normality and convexity. Linear elastic stress-strain relations. Generalized Hooke's law. A plane of symmetry. Two planes of symmetry (orthotropic symmetry). Transverse and cubic isotropies. Full isotropy. Isotropic linear elastic stress-strain relations. Tensor forms. Three-dimensional matrix forms. Plane stress case. Plane strain case. Axisymmetric case. Isotropic nonlinear elastic stress-strain relations based on total formulation. Nonlinear elastic model with secant moduli. Cauchy elastic model. Hyperelastic (green) model. Isotropic nonlinear elastic stress-strain relations based on incremental formulation. Nonlinear elastic model with secant muduli. Cauchy elastic model. Hyerelastic model. Hypoelastic model. Summary. References. 4. Perfect Plasticity and Modeling. Introduction. Deformation theory. An illustrative example. Variable moduli models. Flow theory. Yield criteria. Flow rule. Basic requirements. Perfect plasticity models. Tresca and von Mises models. Coulomb model. Drucker-Prager model. Prandtl-Reuss stress-strain relations. Generalized stress-strain relations. Stiffness formulation. General description. Stiffness coefficients. Summary. References. 5. Hardening Plasticity and Modeling. Introduction. Flow theory. Loading function. Hardening rule. Flow rule. Drucker's postulate. Hardening plasticity models. Lade-Duncan model. Lade model. Nested yield surface models. Generalized multi-surface models. Bounding surface models. Prandtl-Reuss stress-strain relations. Prandtl-Reuss equations. Matrix form of Prandtl-Reuss equations. Generalized stress-strain relations. Incremental stress-strain relations. Isotropic hardening. Kinematic hardening. Mixed hardening. Stiffness formulation. General description. Stiffness coefficients. Summary. References. PART III.