  The purpose of continuum plasticity models is to efficiently predict the
behavior of structures beyond their elastic limits. The purpose of multiscale
materials science models, among them crystal plasticity models, is to
understand the material behavior and design the material for a given target.
The current successful continuum hyperelastoplastic models are based in the
multiplicative decomposition from crystal plasticity, but significant
differences in the computational frameworks of both approaches remain, making
comparisons not straightforward.
  In previous works we have presented a theory for multiplicative continuum
elastoplasticity which solved many long-standing issues, preserving the
appealing structure of additive infinitesimal Wilkins algorithms. In this work
we extend the theory to crystal plasticity. We show that the new formulation
for crystal plasticity is parallel and comparable to continuum plasticity,
preserving the attractive aspects of the framework: (1) simplicity of the
kinematics reaching a parallelism with the infinitesimal framework; (2)
possibility of very large elastic strains and unrestricted type of hyperelastic
behavior; (3) immediate plain backward-Euler algorithmic implementation of the
continuum theory avoiding algorithmically motivated exponential mappings, yet
preserving isochoric flow; (4) absence of Mandel-type stresses in the
formulation; (5) objectiveness and weak-invariance by construction due to the
use of flow rules in terms of elastic corrector rates. We compare the results
of our crystal plasticity formulation with the classical formulation from
Kalidindi and Anand based on quadratic strains and an exponential mapping
update of the plastic deformation gradient.
