This work makes use of the recently proposed second-order nonlinear homogenization model (SOM) for (visco)plastic porous materials 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 and is capable of handling general "ellipsoidal" void shapes (i.e., particulate microstructures with more general orthotropic overall anisotropy) and general three-dimensional loading conditions.