A modification of Prager’s hardening rule

Non-Associated Plasticity for Soils, Concrete and Rock

“…As in the preceding chapters, the plastic strain rate is derived from a plastic potential g: (9.6) To determine the multiplier A, we again make use of the consistency condition, which now reads: (9.7) N ow, we must make an assumption as to the direction of U. One ofthe most widely used assumptions is (Ziegler, 1959), a = scalar", ((f -a) (9.8) with the subsidiary assumption that:…”

Elastic-plastic-creep-large strain analysis at elevated temperature by the finite element method

“…In contrast , the kinematic hardening model of Prager-Ziegler [ 4 ] proposes that the yield surface translates as a ri gid shape during plasti c fl ow ; the di rection of translation being given by a vector connecting the curren t center of the yield surface and the current stress state . This gives rise to an i deal Bauschinger effect in which the reverse yield stress is l owered by an amoun t equa l to the prior strain hardening.…”

Identification of nonlinear kinematic hardening constitutive model parameters using the virtual fields method for advanced high strength steels

“…Among these models, kinematic hardening has been most exclusively employed. The early form that was specifically proposed to represent the Bauschinger effect presumes the yield surface translates in stress space while its shape is maintained (Prager, 1949;Ziegler, 1959). Later on, more comprehensive non-linear kinematic hardening models that combine both translation and expansion of the yield surface were developed and found to be suitable for the prediction of material behavior under cyclic loading conditions (Chaboche, 1986;Dafalias and Popov, 1975;Frederick and Armstrong, 2007;Ohno and Wang, 1993;Yoshida and Uemori, 2002).…”