Influence of Explicit and Implicit Integration of Hyperelastic-Plastic Combined Hardening Models on the Springback in Sheet Forming

Abstract

In this paper, we investigate the computational efficiency of explicit and implicit integration schemes for hyperelastic-plastic combined hardening plasticity and examine the influence on the simulated springback in sheet metal forming. Due to the deviatoric character of the evolution equations, the finite strain combined hardening model discussed here is integrated by means of the exponential map algorithm in order to fulfil plastic incompressibility. We focus here on different possibilities of evaluating the exponential tensor functions of the material model. One option is to use the spectral decomposition to evaluate the exponential tensor functions in closed form. Alternatively, the latter functions can be evaluated by Taylor series expansion. Furthermore, we examine the potential of an explicit formulation of elasto-plasticity with combined hardening regarding accuracy and efficiency. The material model equations have been implemented as user material subroutines UMAT and VUMAT for use in the commercial solvers ABAQUS/Standard and ABAQUS/Explicit, respectively. The numerical models are applied to the finite element simulation of draw bending, where the forming step is simulated both in implicit and explicit manner, whereas the ensuing springback step is carried out only implicitly.