Strongly objective numerical implementation and generalization of a unified large inelastic deformation model with a smooth elastic–inelastic transition

In the present work, a general theoretical framework for modeling a smooth elastic inelastic transition for large deformations of rate independent elastic–plastic and rate dependent elastic–viscoplastic materials is proposed. Generally speaking, in classical rate independent elastic–plastic models the transition from the elastic regime to the plastic regime is sharp, while in the present model this transition is smooth and both rate independent and rate dependent models are characterized by overstress. A finite element formulation has been developed for the general plasticity model, which integrates the evolution equations and formulates the tangent stiffness in terms of the state variables and the relative deformation gradient during a time step. In particular, this formulation is independent of a total strain measure and arbitrariness of the specification of a reference configuration. A number of large deformation example problems, which examine and verify the implementation of the developed finite element, show that the integration scheme for the elastic distortional deformation is strongly objective and demonstrate the capability of the formulation in modeling realistic problems like necking of cylindrical bar.