Solution procedures for J3 plasticity and viscoplasticity Original Research Article

A solution strategy for plasticity and viscoplasticity models with isotropic yield surfaces depending upon all the principal invariants of the stress tensor is presented. Basically, it requires the inversion of a fourth-order positive definite tensor G both for the solution of the constitutive problem and for the evaluation of the consistent tangent operator. It is proved that the assumption of isotropic elastic behaviour and the isotropy of the yield criterion entail an explicit representation formula for G−1 as linear combination of dyadic and square tensor products. Further, an analogous representation formula for the consistent tangent operator is provided. By exploiting basic composition rules between dyadic and square tensor products along with Rivlinʹs identities for tensor polynomials, all tensor operations required to compute the coefficients of the adopted representation formula for G−1 are carried out in intrinsic form. It is thus shown that the relevant computational burden essentially amounts to solving a linear system of order three. The performances of the proposed approach are illustrated by means of some numerical examples referred to the Argyris failure criterion.