ON THE APPLICATION OF MULTI-STEP INTEGRATION METHODS TO INFINITESIMAL ELASTO-PLASTICITY
P. PAPADOPOULOS and R. L. TAYLOR Int. J. Num. Meth. Engr. 37, pp. 3169-3184, (1994)

Abstract
This article proposes an implicit algorithm for time integration of the differential/algebraic equations of small-deformation elasto-plasticity in strain space. The algorithm employs a two-step backwards differentiation formula and a standard operator-split procedure. Second-order accuracy and non-linear stability are established under appropriate constitutive restrictions. The algorithm is implemented for the model of J2-plasticity and numerical simulations are conducted that illustrate its applicability and accuracy.