A model of finite strain viscoplasticity based on unified constitutive equations. Theoretical and computational considerations with applications to shells Original Research Article

A model of multiplicative finite strain viscoplasticity is developed. Hereby the elastic internal potential is assumed to depend quadratically on the elastic strain measure Ce by means of corresponding invariants. Hence, possible extension of the model to take anisotropy into account is straightforward. The evolution equation of the unified type due to Bodner and Partom [ASME J. Appl. Mech. 42 (1975) 385] are modified so as to fit into the framework adopted. The numerical treatment of the problem is fully developed. Specifically, the algorithmic aspects of the resulting non-additive structure are intensively discussed. Hereby, the treatment of the exponential map of a non-symmetric argument is of a central importance. Two consistent methods are developed. Various applications to shell problems are considered. Hereby, a shell theory with seven degrees of freedom together with a 4-node enhanced strain finite element formulation are used. A central feature of the shell formulation is its eligibility to the application of a three-dimensional constitutive law.