On precipitate induced hardening in crystal plasticity: algorithms and simulations

A crystal elasto-plastic setting was suggested by the authors in Han et al. [Int. J. Plasticity (in press)] to account for precipitate shapes and structure in the kinematic hardening description. In this article, the corresponding elastic–plastic rate independent algorithmic treatment is derived and numerical simulations performed. For the convenience of the computational derivation and implementation, the material formulation is formulated in the unrotated intermediate configuration mapped by the plastic part of the deformation gradient. Several descriptions for the evolution equations, based on the elastic inclusion model [Acta Metal. 29 (1981) 1797] of the kinematic hardening, are suggested and discussed. Finally, some numerical examples are presented to assess the performance of the suggested model and its rate-independent algorithmic treatment.