ABSTRACT
This chapter provides an introduction to the topic of rate-independent, small-strain plasticity. The basic finite element procedure for solving small-strain plasticity problems is based on Newton's method, in which the resulting linearized system of algebraic equations is solved in an iterative manner. One of the major objectives in any plasticity theory is to come up with a multiaxial relationship between the stress increments and the total strain increments during plastic loading. Arguably the main ingredient in any mathematical theory of plasticity is the yield condition. The yield condition is also commonly referred to as a yield function or yield surface. In the development of the classical small-strain plasticity theory, Richard von Mises proposed the existence of a plastic potential function. The chapter discusses the isotropic and kinematic hardening rules. It also serves as an excellent avenue through which to present a standard finite element procedure for solving nonlinear problems in solid mechanics.
