SECOND ORDER INTEGRATION ALGORITHMS FOR J2 PLASTICITY WITH GENERALIZED ISOTROPIC/KINEMATIC HARDENING

In this work four algorithms are presented for the integration of equations governing the behavior of von Mises material in plastic limit. Two of them are single-step and the others are double-step algorithms. Single-step algorithms are straight forward extension of backward Euler method or midpoint rule while double-step algorithms are a combination of two. In past similar algorithms were proposed for special cases of isotropic/kinematic hardening; however the algorithms presented in this work are applicable to general isotropic/kinematic hardening laws. Theoretical as well as numerical aspects are presented for all integration schemes and elaborated for double-step algorithms which are less explored in the literature. A comparison is made between the presented algorithms and the classical backward Euler method.