  This article deals with the mathematical derivation and the validation over
benchmark examples of a numerical method for the solution of a finite-strain
holonomic (rate-independent) Cosserat plasticity problem for materials,
possibly with microstructure. Two improvements are made in contrast to earlier
approaches: First, the micro-rotations are parameterized with the help of an
Euler-Rodrigues formula related to quaternions. Secondly, as main result, a
novel two-pass preconditioning scheme for searching the energy-minimizing
solutions based on the limited memory Broyden-Fletcher-Goldstein-Shanno
quasi-Newton method is proposed that consists of a predictor step and a
corrector-iteration. After outlining the necessary adaptations to the model,
numerical simulations compare the performance and efficiency of the new and the
old algorithm. The proposed numerical model can be effectively employed for
studying the mechanical response of complicated materials featuring large size
effects.

Computational Engineering, Finance, and Science;Materials Science