Second order integration algorithms for von-Mises plasticity with a non-linear kinematic hardening mechanism

Two second-order numerical schemes for von-Mises plasticity with a combination of linear isotropic and nonlinear kinematic hardening are presented. The first scheme is the generalized midpoint integration procedure, originally introduced by Ortiz and Popov in 1985, detailed and applied here to the case of Armstrong–Frederick nonlinear kinematic hardening. The second algorithm is based on the constitutive model exponential-based reformulation and on the integration procedure previously introduced by the authors in the context of linearly hardening materials. There are two main targets to the work. Firstly, we wish to extensively test the generalized midpoint procedure since in the scientific literature no thorough numerical testing campaign has been carried out on this second-order algorithm. Secondly, we wish to extend the exponential-based integration technique also to nonlinear hardening materials. A wide numerical investigation is carried out in order to compare the performance of the two methods.