Numerical simulation of springback using an extended return mapping algorithm considering strain dependency of elastic modulus

Several studies have reported that the elastic modulus decreases during elastoplastic deformation. However, the return mapping algorithms commonly used to implement the elastoplastic constitutive equations into finite element programs assume that the elastic modulus remains constant during plastic deformation. In order to consider the decrease of elastic modulus in elastoplastic constitutive models, the return mapping algorithms need to be generalized. In this study, a numerical procedure was developed for implementation of elastoplastic constitutive laws assuming that the elastic modulus was defined as a function of effective plastic strain. Using the developed numerical procedure, the Hillʹs quadratic yield function and the combined isotropic-nonlinear kinematic hardening model was implemented as a user subroutine for ABAQUS commercial finite element package. Different numerical tests were carried out to evaluate the performance of the developed algorithm. The results showed that the algorithm was robust and as accurate as the other return mapping algorithms. Finally, the model was used to simulate both the forming stage and the subsequent springback of a U-shaped part made of DP600 steel. The results showed that the accuracy of springback simulation considerably improved when the decrease of elastic modulus was described in the model.