Chapter 4. Plasticity
4.1. Ideal Plasticity 97
4.1.1. General formulation 97
4.1.2. Slip line theory 100
4.1.3. Beams and plates 102
4.1.4. Anisotropy and other complexities beyond ideal plasticity103
4.2. Hardening Plasticity 105
4.2.1. Deformation theory 105
4.2.2. Isotropic hardening 105
4.2.3. Kinematic hardening 107
4.2.4. Metal fatigue 109
4.3. Viscoplasticity 109
4.4. Large plastic deformation 110
4.4.1. Objectivity 111
4.4.2. Strain and stress rates 111
4.4.3. Multiplicative decomposition 112
4.5. Plastic limit theorems 113
4.6. Shakedown theorems for perfectly-elastic-plastic bodies 116
4.6.1. Introduction 116
4.6.2. Shakedown static theorem 118
4.6.3. Koiter's shakedown kinematic theorem 121
4.6.4. Modified shakedown kinematic theorem 121
4.6.5. Plastic limit case 126