On shakedown theorems in hardening plasticity

The model of generalized standard materials gives a convenient framework to extend Koiter's shakedown theorems into hardening plasticity. The extension of the static shakedown theorem (Melan–Koiter's theorem), proposed previously in [5], is considered here. It leads to the definition of safety coefficients in hardening plasticity by duality. Static and kinematic approaches are discussed for the models of isotropic hardening, of linear kinematic hardening (Ziegler–Prager's model) and of limited kinematic hardening. This discussion also leads to an extension of Koiter's kinematic shakedown theorem and to a second kinematic coefficient.