A comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticity

The paper presents a comparative discussion of stress update algorithms for single-crystal plasticity at small strains. The key result is a new uni ed fully implicit multisurface-type return algorithm for both the rateindependent and the rate-dependent setting, endowed with three alternative approaches to the regularization of possible redundant slip activities. The fundamental problem of the rate-independent theory is the possible ill condition due to linear-dependent active slip systems. We discuss three possible algorithmic approaches to deal with this problem. This includes the use of alternative generalized inverses of the Jacobian of the currently active yield criterion functions as well as a new diagonal shift regularization technique, motivated by a limit of the rate-dependent theory. Analytical investigations and numerical experiments show that all three approaches result in similar physically acceptable predictions of the active slip of rate-independent singlecrystal plasticity, while the new proposed diagonal shift method is the most simple and e cient concept