ABSTRACT
This chapter presents an introduction to the mathematical theory of plasticity. It presents an introduction to the rate-independent, isothermal theory of plasticity. The chapter describes two specific simple hardening models (isotropic hardening and kinematic hardening) that can be used to describe the evolution of the yield surface with accumulated plastic strain. Uniaxial stress tests on metals are probably the simplest and most commonly performed material tests. Elastic strains will truly be small in most cases where a plasticity material model is appropriate; however, large plastic strains can occur in practically important stress analysis situations. The shape of the yield surface is constrained by certain symmetry requirements, invariance under coordinate rotation, conservation laws, and material stability conditions. The chapter also presents additional geometric interpretations of the elastoplastic stress. A tension–torsion test was originally designed for testing of metals in order to understand their behavior in multiaxial stress states.
