Modeling and characterization of cyclic relaxation and ratcheting using the distributed-element model

Constitutive modeling of cyclic relaxation and ratcheting (cumulative inelastic deformation) is developed on the basis of the distributed-element model (DEM). Although the original DEM is capable of describing general, elastic–plastic behavior for cyclically stabilized materials, it has the inadequacy of not being able to account for the effect of cyclic relaxation and ratcheting. By introducing the nonlinear kinematic hardening rule proposed by Armstrong and Frederick into element behavior of the DEM, the model becomes effective in characterizing the behavior of cyclic relaxation and ratcheting. Validation of the modified DEM is conducted by simulating cyclic behavior of various metal materials, including CS 1018, heat-treated rail steel, and Grade 60 steel. The results show that the modified DEM demonstrates realistic behavior of materials in both uniaxial and biaxial cyclic relaxation and ratcheting. Furthermore, detailed investigation of element behavior in the model provides us with additional insight into complex behavior and characteristics of materials in cyclic relaxation and ratcheting.