Efficient and robust constitutive integrators for single-crystal plasticity modeling

TL;DR

This paper introduces an explicit constitutive update algorithm for single-crystal plasticity that is significantly faster than traditional implicit methods, enabling efficient dynamic deformation simulations with minimal accuracy loss.

Contribution

The work recasts an implicit constitutive update into an explicit form, achieving 5-6 times faster updates and up to 50 times faster overall simulations, with added subcycling for further efficiency.

Findings

Explicit model is 5-6 times faster per step.

Overall simulation speed up to 50 times with explicit model.

Performance improvements extend to polycrystal simulations.

Abstract

Simulations of the dynamic deformations of metal samples require elastic-plastic constitutive updates of the material behavior to be performed over a small time step between updates, as dictated by the Courant condition. Depending on the deformation conditions, the converged time step becomes short (~$10^{-9} s$ or less). If an implicit constitutive update is applied to this class of simulation, the benefit of the implicit update is negated, and the integration is prohibitively slow. The present work recasts an implicit update algorithm into an explicit form, for which each update step is five to six times faster, and the compute time required for a plastic update approaches that needed for a fully-elastic update. For dynamic loading conditions, the explicit model is found to perform an entire simulation up to 50 times faster than the implicit model. The performance of the explicit model is enhanced by adding a subcycling algorithm to the explicit model, by which the maximum time step between constitutive updates is increased an order of magnitude. These model improvements do not significantly change the predictions of the model from the implicit form, and provide overall computation times significantly faster than the implicit form over finite-element meshes. These modifications are also applied to polycrystals via Taylor averaging, where we also see improved model performance.