Viscoplasticity model at finite deformations with combined isotropic and kinematic hardening

In this work, we construct a phenomenological constitutive model of viscoplasticity at finite strains, which generalizes the classical Perzyna or Duvaut–Lions models to finite strains. The latter is accomplished with a minimum number of hypothesis, including the multiplicative decomposition of deformation gradient, a definition of the elastic domain and finally a penalty-like, viscoplastic regularization of the principle of maximum plastic dissipation. The model is extended to include the isotropic and kinematic hardening of Prager–Ziegler type. Numerical computation of the viscoplastic flow at finite strain is also discussed, along with the corresponding simplification resulting from a convenient choice of the logarithmic strain measure. Several illustrative numerical examples are presented in order to demonstrate the ability of the proposed model to remove the deficiencies of some currently used models.