Structural Plasticity

1 One-Dimensional Stress-Strain Analysis.- 1.1 Uniaxial Behaviors.- 1.2 Basic Relations.- 1.3 Idealized Stress-Strain Relationships.- 1.4 Hardening Rules.- 1.5 Stress-Strain Response Problems.- 1.6 Fixed-End Bar Problems.- 1.7 Stepped and Tapped Bar Problems.- 1.8 Three-Bar Structure Problems.- 1.9 Three-Bar Truss Problems.- 2 One-Dimensional Stress-Strain Analysis Software.- 2.1 Formulation of PLASTIC1.- 2.2 Algorithms.- 2.3 Implementation of PLASTIC1.- 2.4 User’s Manual of PLASTICI.- 2.5 Problems Associated with Hardening Parameters.- 2.6 Problems Associated with Hardening Rules.- 2.7 Source Code Listing of PLASTIC1.- 3 Elastic Stress and Strain Analysis.- 3.1 Stress Tensor.- 3.2 Principal Stresses and Stress Invariants.- 3.3 Deviatoric Stress Tensor and Its Invariants.- 3.4 Geometric Representation of Stress States.- 3.5 Equilibrium Equations.- 3.6 Strain Tensor.- 3.7 Principal Strains and Strain Invariants.- 3.8 Deviatoric Strain Tensor and Its Invariants.- 3.9 Compatibility Equations.- 3.10 Generalized Hooke’s Law.- 3.11 Decomposition of Stress-Strain Relations.- 3.12 Basic Equations in Cylindrical and Spherical Coordinates.- 4 Yield Criteria.- 4.1 Representation of Yield Criteria.- 4.2 Hydrostatic-Pressure-Independent Materials.- 4.3 Hydrostatic-Pressure-Dependent Materials.- 4.4 Tresca and von Mises Problems.- 4.5 Mohr-Coulomb Problems.- 4.6 Drucker-Prager Problems.- 4.7 Tension Cut-Off Problems.- 5 Perfectly Plastic Stress Analysis.- 5.1 General Aspects.- 5.2 Loading Criterion.- 5.3 Plastic Potential and Flow Rule.- 5.4 Complete Perfectly Plastic Constitutive Relation.- 5.5 Thin-walled Vessel Problems.- 5.6 Plastic Zone Near Crack Tip Problems.- 5.7 Thick-walled Vessel Problems.- 5.8 Incremental Stress-Strain Relation Problems.- 5.9 Source Code Listing of PLASTIC_ZONE.- 6 Hardening Plastic Stress Analysis.- 6.1 Introduction.- 6.2 Deformational Theory.- 6.3 Loading Surfaces and Loading Criteria.- 6.4 Flow Rules.- 6.5 Hardening Rules.- 6.6 Effective Stress and Effective Plastic Strain.- 6.7 Incremental Stress-Strain Relationships.- 6.8 Problems Using Incremental Theory.- 6.9 Problems Using Deformational Theory.