Stable splitting scheme for general form of associated plasticity including different scales of space and time

An efficient implementation of the operator split procedure for boundary value solution with plastic flow computation is presented for a general form of associated plasticity model. We start with the general form of phenomenological model of plasticity where the yield criterion is not restricted to a simple (quadratic) form, and the elasticity tensor does not have constant entries. We then turn to the multi-scale model of plasticity which employs the fine scale representation of the plastic deformation along with the homogenization procedure for stress computation. We also visit the plasticity model with rate sensitive plastic response where plastic flow computation is carried out at fine scale in time. We proved herein the sufficient and necessary conditions for the proposed operator split procedure to converge, for any such general form of associated plasticity. Moreover, we presented a systematic manner for constructing the main ingredients for the plastic flow computation and the global Newton's iteration, such as the consistent elastoplastic tangent.