A robust and efficient substepping scheme for the explicit numerical integration of a rate-dependent crystal plasticity model

This paper describes the development of efficient and robust numerical integration schemes for ratedependent
crystal plasticity models. A forward Euler integration algorithm is first formulated. An integration
algorithm based on the modified Euler method with an adaptive substepping scheme is then proposed, where
the substepping is mainly controlled by the local error of the stress predictions within the time step. Both
integration algorithms are implemented in a stand-alone code with the Taylor aggregate assumption and
in an explicit finite element code. The robustness, accuracy and efficiency of the substepping scheme are
extensively evaluated for large time steps, extremely low strain-rate sensitivity, high deformation rates and
strain-path changes using the stand-alone code. The results show that the substepping scheme is robust and
in some cases one order of magnitude faster than the forward Euler algorithm. The use of mass scaling
to reduce computation time in crystal plasticity finite element simulations for quasi-static problems is also
discussed. Finally, simulation of Taylor bar impact test is carried out to show the applicability and robustness
of the proposed integration algorithm for the modelling of dynamic problems with contact.