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

A new computational model for the rate-independent elasto-plastic solids characterized by yield surfaces containing singularities and general nonlinear isotropic hardening is presented. Within the context of fully implicit return mapping algorithms, a numerical scheme for integration of the constitutive equations is formulated in the space of principal stresses. As a direct consequence of the principal stress approach, the representation of a yield surface is cast in terms of ‘optimal’ parameterization, which for the Tresca yield criterion takes a simple linear form. The associated return mapping equations then reduce to a remarkably simple format. In addition, due to 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 eigenvalues are expressed in terms of the eigenvalues of the argument. This observation leads to a simple closed form derivation of the consistent tangent moduli associated with the described integration algorithms. The extension of the present model to finite strains is carried out following standard multiplicative plasticity described in terms of logarithmic stretches and exponential approximation to the flow rule. The efficiency and robustness of the computational model are illustrated on a range of numerical examples.