A new computational model for Tresca plasticity at finite strains with an optimal parametrization in the principal space

A new computational model for the rate-independent elasto-plastic solids ch aracterized by yield surfaces containing singularities and general nonlinea r isotropic hardening is presented. Within the context of fully implicit re turn mapping algorithms, a numerical scheme for integration of the constitu tive equations is formulated in the space of principal stresses. As a direc t consequence of the principal stress approach, the representation of a yie ld surface is cast in terms of 'optimal' parameterization, which for the Tr esca yield criterion takes a simple linear form. The associated return mapp ing equations then reduce to a remarkably simple format. In addition, due t o assumed isotropy of the models, the associated algorithmic (incremental) constitutive functionals can be identified as particular members of a class of isotropic tensor functions of one tensor in which the function eigenval ues are expressed in terms of the eigenvalues of the argument. This observa tion leads to a simple closed form derivation of the consistent tangent mod uli associated with the described integration algorithms. The extension of the present model to finite strains is carried out following standard multi plicative plasticity described in terms of logarithmic stretches and expone ntial approximation to the flow rule. The efficiency and robustness of the computational model are illustrated on a range of numerical examples. (C) 1 999 Elsevier Science S.A. All rights reserved.