ABSTRACT
The evolution of implicit integration algorithms dates back to the pioneering work of Wilkins (1964). The algorithm that he developed was actually a backward Euler type of algorithm for the integration of first order ordinary differential equations as a function of time. Backward Euler algorithm has been used successfully in the work of many authors and has proven its applicability in many research and commercial Softwares. Midpoint rule algorithm was first proposed in the work of Ortiz & Popov (1985).They also presented a method for investigating the stability of this type of algorithm which was later modified and corrected in the work of Simo & Govindjee (1991). Artioli et al. 2007 used double step methods for linear hardening and a type of nonlinear hardening in some detail. Jahanshahi (2012) modified second order integration algorithms to account for generalized form of isotropic hardening and formulated a variant of double step integration scheme for nonlinear hardening, Jahanshahi (2012).
