Concept of the limit yield condition in shakedown theory

The concept of the limit yield condition is introduced which makes possible the extension of both the static (Melan) shakedown conditions, and the necessary kinematic (Koiter) one to a class of classical constitutive material models with internal variables. This class includes material models with both bounded and unbounded nonlinear isotropic strain-hardening. It is assumed that the yield conditions are convex with respect to stresses for all admissible values of the internal variables, but convexity in the internal variables is not assumed. Connections are established between the response of elastic perfectly plastic bodies to cyclic loading and that of bodies with internal variables. A method for estimating the limit yield condition is developed, and an example of this application is given.