Modeling the Bauschinger effect is usually accomplished by introducing a second-order
back-stress or directional hardening tensor. The objective of this paper is to
propose a simpler scalar model of the Bauschinger effect based on a scalar directional
hardening parameter that is determined by integration of an evolution equation.
The behavior of this scalar model is compared to a tensorial model for a number of
load cases. Strongly objective numerical algorithms are developed for integrating the
evolution equations for both the tensorial and scalar models. Also, a consistent tangent
is developed for both models. Obviously, the numerical implementation of the scalar
model is significantly less complicated than for the tensorial model. Examples show
that the tensorial and scalar models predict the same results for cyclic proportional
triaxial extension and triaxial compression loadings. In contrast, the tensorial model
predicts a Bauschinger effect for cyclic proportional pure torsion loading which is
not predicted by the scalar model. More complicated examples with nonproportional
loading paths and inhomogeneous deformations indicate that, relative to the tensorial
model, the scalar model accounts for directional hardening fairly well and the simplicity
of the model makes it an attractive option to add to isotropic hardening models.
