On the application of multi‐step integration methods to infinitesimal elastoplasticity

This article proposes an implicit algorithm for time integration of the differential/algebraic equations of small‐deformation elastoplasticity 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 J 2 ‐plasticity and numerical simulations are conducted that illustrate its applicability and accuracy.