Computing the asymptotic cyclic response of elastoplastic solids with nonlinear kinematic hardening

We propose a direct method to compute the steady state response to cyclic loadings of elastoplastic solids with Armstrong-Frederick nonlinear kinematic hardening. The algorithm obtains the elastoplastic asymptotic cyclic response without true incremental integration. The method performs much faster than using the step-by-step procedure until stabilization. Including nonlinear kinematic hardening in this asymptotic analysis allows modeling the ratcheting phenomenon, which is important in safety assessment of structures under variable loadings. To the best of the authors knowledge, this is the first direct procedure for computing the asymptotic cyclic response of elastoplastic solids with nonlinear kinematic hardening.