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 J2-plasticity and numerical simulations are conducted that illustrate its applicability and accuracy.

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