This work makes use of the recently proposed second-order nonlinear homogenization model (SOM) for (visco)plastic porous materials [1] to study the influence of the Lode parameter and the stress triaxiality on the failure of metallic materials. This model is based on the "second-order" or "generalized secant" homogenization method [2] and is capable of handling general "ellipsoidal" microstructures (i.e., particulate microstructures with more general orthotropic overall anisotropy) and general three-dimensional loading conditions.

See http://hal.archives-ouvertes.fr/docs/00/59/26/93/ANNEX/r_A1B5O25U.pdf