Viscoplasticity Using Dual Variables

Constitutive relations describing plastic and viscoplastic material behaviour at finite deformations are presented. The material response is assumed to exhibit kinematic hardening effects. Evolution equations governing the response of kinematic hardening are derived as sufficient conditions in order for the dissipation inequality to be satisfied in every process. The main difference between the present work and other contributions in this area is the choice of the variables and of the time derivatives used to formulate the theory. The numerical integration algorithm used for the implementation of the models into the Finite Element code ABAQUS briefly is discussed. The pressurized thick-walled tube is analysed to demonstrate second order effects.