A return map algorithm for general isotropic elasto/visco-plastic materials in principal space

We describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto/visco-plastic models whose yield function incorporates the third stress invariant J3. The developments presented are based upon original results, proved in the paper, concerning the derivatives of eigenvalues and eigenprojectors of symmetric second-order tensors with respect to the tensor itself and upon an original algebra of fourth-order tensors A obtained as second derivatives of isotropic scalar functions of a symmetric tensor argument A. The analysis, initially referred to the small-strain case, is then extended to a formulation for the large deformation regime; for both cases we provide a derivation of the consistent tangent tensor which shows the analogy between the two formulations and the close relationship with the tangent tensors of the Lagrangian description of large-strain elastoplasticity.