Spurious softening in the macroscopic response predicted by the additive tangent Mori–Tanaka scheme for elastic–viscoplastic composites

Abstract

The Mori–Tanaka (MT) scheme is a well-established mean-field model that combines simplicity and good predictive capabilities. The additive tangent MT scheme is a popular variant of the method that is suitable for elastic–viscoplastic composites. This work is concerned with the analysis of some intrinsic features of the additive tangent MT scheme, in particular, of spurious softening in the macroscopic response that may be encountered when the Perzyna-type viscoplasticity model is used. The resulting non-monotonic macroscopic stress–strain response is clearly non-physical, but it also has a negative impact on the efficiency and robustness of the MT model when it is used as a local constitutive model in concurrent multiscale finite-element computations. As shown in the paper, the spurious softening is more pronounced when the so-called soft isotropization is employed to compute the viscoplastic Hill tensor, but it is also observed, although for a much narrower range of material parameters, in the case of the hard isotropization and when no isotropization is applied. Moreover, the softening is promoted at low strain rates, for high elastic contrast, and for high volume fractions of inclusions. Nevertheless, if the soft isotropization is avoided, the additive tangent MT scheme proves to be a feasible and computationally robust mean-field model that can be successfully employed in finite-element computations.