Cyclic loading of beams based on the Prager and Frederick–Armstrong kinematic hardening models

The kinematic hardening theory of plasticity based on the Prager and Frederick–Armstrong models are used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. The beam material is assumed to follow non-linear strain hardening property. The materialʹs strain hardening curves in tension and compression are assumed to be both identical for the isotropic material and different for the anisotropic material. A numerical iterative method is used to calculate the stresses and plastic strains in the beam due to cyclic loadings. The results of the analysis are checked with the known experimental tests. It is concluded that the Prager kinematic hardening theory under deformation controlled conditions, excluding creep, results into reversed plasticity. The load controlled cyclic loading under the Prager kinematic hardening model with isotropy assumption results into reversed plasticity. Under anisotropy assumption of tension/compression curve, this model predicts ratcheting. On the other hand, the Frederick–Armstrong model predicts ratcheting behavior of the beam under load controlled cyclic loading with non-zero mean load. This model predicts reversed plasticity under the load controlled cyclic loading with zero mean load, and deformation controlled cyclic loading.