Computational issues of general isotropic elastoplastic models

We illustrate the principal space specialization of a recently proposed solution strategy for elastoplasticity with isotropic yield surfaces depending upon all the three invariants of the stress tensor. The main issue to address, for computing both the return map solution and the consistent tangent operator, is the inversion of a fourth-order positive de nite tensor G. This task has been already accomplished by the authors by providing, in the given reference frame, an explicit representation formula for G􀀀1 as linear combination of dyadic and square tensor products. We here adopt a di erent approach by expressing G in matrix form with respect to the reference frame associated with the eigenvectors of the stress tensor. The latter procedure, di erently from the former, requires the transformation of tensorial quantities between the given reference frame and the principal one; this is however compensated by the fact that the coe cients of the spectral representation of G􀀀1 can be obtained by inverting a positive de nite 3x3 matrix. Accordingly, the spectral representation of the consistent tangent operator can be obtained by straightforward matrix products between 3x3 matrices. The numerical performances of the two strategies are demonstrated with reference to a typical benchmark problem.