Fundamentals of Plasticity in Geomechanics

Contents Preface Chapter 1. Basic concepts of the theory of plasticity 1.1 Typical approximations of uniaxial response of the material 1.2 The notion of generalized yield/failure criterion 1.3 Generalization of the concept of elastic-perfectly plastic and strain hardening material 1.4 Determination of plastic strain; deformation and flow theories of plasticity 1.5 Review of fundamental postulates of plasticity; uniqueness of the solution Chapter 2. Elastic-perfectly plastic formulations in geomechanics 2.1 General considerations 2.2 Geometric representation of the failure surface 2.3 Selection of stress invariants for the mathematical description 2.4 Typical failure criteria for geomaterials 2.4.1 Mohr-Coulomb failure criterion 2.4.2 Drucker-Prager and other derivative criteria 2.4.3 Modified criteria based on smooth approximations to Mohr-Coulomb envelope 2.4.4 Non-linear approximations in meridional section 2.5 Derivation of constitutive relation 2.5.1 Matrix formulation 2.6 Consequences of a non-associated flow rule Chapter 3. Isotropic strain-hardening formulations 3.1 'Triaxial' tests and their mathematical representation 3.1.1 Mohr-Coulomb criterion in 'triaxial' space 3.1.2 On the behaviour of a perfectly plastic Mohr-Coulomb material 3.1.3 Review of typical mechanical characteristics of granular materials 3.2 Volumetric hardening; Critical State model 3.2.1 Formulation in the 'triaxial' {p,q} space 3.2.2 Comments on the performance 3.2.3 Generalization and specification of the constitutive matrix 3.3 Deviatoric hardening model 3.3.1 Formulation in the 'triaxial' {p,q} space 3.3.2 Comments on the performance 3.3.3 Generalization and specification of the constitutive matrix 3.4 Combined volumetric-deviatoric hardening 3.5 Specification of constitutive matrix under undrained conditionsa Chapter 4. Combined isotropic-kinematic hardening rules 4.1 Bounding surface plasticicty; volumetric hardening framework 4.1.1 Formulation in the 'triaxial' {p,q} space 4.1.2 Comments on the performance 4.1.3 Generalization and specification of the constitutive matrix 4.2 Bounding surface plasticicty; deviatoric hardening framework 4.2.1 Formulation in the 'triaxial' {P,Q} space 4.2.2 Comments on the performance 4.2.3 Generalization and specification of the constitutive matrix Chapter 5. Numerical integration of constitutive relations 5.1 Euler's integration schemes 5.2 Numerical integration of {p,q} formulation 5.2.1 Stress-controlled scheme 5.2.2 Strain-controlled schemes 5.3 Numerical examples of integration in {p,q}-space 5.3.1 Critical State model; drained p=const. compression 5.3.2 Deviatoric hardening model; drained 'triaxial' compression 5.3.3 Deviatoric hardening model; undrained 'triaxial' compression 5.4 General methods for numerical integration 5.4.1 Statement of algorithmic problem 5.4.2 Notion of closest point projection 5.4.3 Return-mapping algorithms Chapter 6. Introduction to limit analysis 6.1 Formulation of lower and upper bound theorems 6.2 Examples for applications of limit theorems in geotechnical engineering Chapter 7. Description of inherent anisotropy in geomaterials 7.1 Formulation of anisotropic failure criteria 7.1.1 Specification of failure criteria based on critical plane approach 7.1.2 Formulation of failure criteria incorporating a microstructure tensor 7.2 Description of inelastic deformation process 7.2.1 Plasticity formulation for critical plane approach 7.2.2 Plasticity formulation incorporating a microstructure tensor 7.2.3 Numerical examples Chapter 8. Experimental trends in the mechanical behaviour of soils and rocks 8.1 Basic mechanical characteristics in monotonic tests under drained conditions 8.1.1 Influence of confining pressure; compaction/dilatancy 8.1.2 Influence of Lode's angle and the phenomenon of strain localization 8.2 Undrained response of granular media; pore pressure evolution, liquefaction 8.3 Basic mechanical characteristics in cyclic tests; hysteresis and liquefaction 8.4 Inherent anisotropy; strength characteristics of sedimentary rocks 8.5 Identification of basic material parameters for soils/rocks 8.5.1 General remarks on identification procedure 8.5.2 Examples involving deviatoric hardening framework Bibliography Appendix: Suggested exercises