Cyclic plasticity using Prager’s translation rule and both nonlinear kinematic and isotropic hardening: theory, validation and algorithmic implementation

Resumen

Finite element analysis of structures under elasto-plastic nonproportional cyclic loadings is useful in seismic engineering, fatigue analysis and ductile fracture. Usual models with nonlinear stress–strain curves in cyclic behavior are based on Mróz multisurface plasticity, bounding surface models or models derived from the Armstrong–Frederick rule. These models depart from the associative Prager’s rule with the main purpose of modeling aspects of cyclic nonlinear hardening. In this paper we develop a model for cyclic plasticity within the framework of the associative classical plasticity theory using Prager’s rule accounting for anisotropic nonlinear kinematic hardening coupled with nonlinear isotropic hardening. We include the validation of the theory against several uniaxial and multiaxial cyclic experiments and an efficient fully implicit radial return algorithm. The parameters of the model are obtained directly by a discretization of the uniaxial stress–strain behavior. Remarkably, both the presented theory and the computational algorithm automatically recover classical bi-linear plasticity and the Krieg and Key algorithm if the user-prescribed stress–strain curve is bilinear.