YAP 616E - Theory of Plasticity

Course Objectives

1. To present the fundamental principles and mathematical methods of plasticity theory
2. To present plasticity models appropriate for different materials and problems
3. To perform limit analysis of various structural elements using plasticity methods
4. To present and implement numerical methods used for solution of plasticity problems

Course Description

Physical foundations of plasticity theory, concepts and definitions. Mathematical foundations, elastic/plastic deformations, stress tensor and its invariants. Incremental and total strain theories of plasticity. Yield criterion, flow rule and hardening/softening rules. Tresca, von Mises, Drucker-Prager and other yield criteria. Isotropic, kinematic and combined hardening rules. Cyclic loading, loading rate and temperature effects. Uniqueness and extremum principles, energy methods. Limit analysis, lower and upper bound theorems. Plastic analysis of frame, plate and shell elements. Dynamic plasticity and viscoplasticity. Numerical solution of plasticity problems using finite difference and finite element methods.