A Finite Element Time Integration Method for the Theory of Viscoplasticity Based on Infinitesimal Total Strain

A forward gradient method is employed in the formulation of a time integration scheme for the theory of viscoplasticity based on total strain. The theory uses a viscosity function and an equilibrium stress-strain diagram to characterize a material in monotonic loading. Eight-noded quadrilateral elements integrated by a 2 × 2 quadrature provide spatial modeling. For a thick-walled, axially constrained cylinder under internal pressure the stability of the proposed integration scheme is demonstrated. It is shown that pressurization rate considerably influences the state of stress in the cylinder. The stresses redistribute with time when the pressure is held constant. For long times an equilibrium solution can be obtained. When a bilinear equilibrium stress-strain diagram with zero work-hardening is chosen, the equilibrium solution is shown to correspond to the elastic-perfectly plastic solution.