Subspace tracking method for non-smooth yield surface

The corners of non-smooth yield surfaces, e.g., Mohr-Coulomb or Hoek-Brown criteria, often cause problems in numerical applications due to the gradient discontinuities, which boil down to the abrupt order interchange of two principal stresses. Nevertheless, when the stress components cross the corners, the principal stresses, which are smoothly dependent on the components of stress tensor, can be smoothly tracked through subspace tracking method. Thus, all the six auxiliary yield functions based on Koiter's rule will be smooth functions of components of stress. Finally, the corner problems are eliminated. As an application, three boundary-value problems (a 3D one-element, a 2D slope with a soft band, and a 3D soil slope) are analyzed to investigate the performance of the proposed method in a non-linear finite element simulation.