FEM Modeling of Beams Cyclic Loading Based on Ziegler-Prager and Armstrong-Frederick Kinematic Hardening Models
In this investigation the behavior of classical beams are simulated by a finite element formulation of the plasticity problem under two major kinematic hardening models. Complete formulation is presented for both load and deformation controlled cases. The proposed finite element formulation uses a variable stiffness matrix in each incremental step reflecting the yield surface movement. Examples are worked out for both the Ziegler-Prager and the Armstrong-Frederick theories, to show the stress-strain behavior under cyclic symmetric and asymmetric flexural loading. The results have been graphically illustrated in plots of the response curves and are compared to the published and experimental ones. It was observed that Ziegler-Prager theory for anisotropic cases with symmetric loading predicts a ratcheting response. While the results show agreement with published ones; it was also observed that the two theories do not show similar responses of reverse plasticity or ratcheting for Euler-Bernoulli beams in all the example cases.
E. Hashemi et al., "FEM Modeling of Beams Cyclic Loading Based on Ziegler-Prager and Armstrong-Frederick Kinematic Hardening Models", Applied Mechanics and Materials, Vols. 110-116, pp. 2838-2846, 2012