On the Use of Explicit and Implicit Exponential Map Algorithms of Finite Strain Combined Hardening Plasticity in the Simulation of Draw Bending

Abstract

The paper investigates the computational efficiency of explicit and implicit integrationschemes for hyperelastic-plastic combined hardening plasticity and examines the influence on thesimulated springback in sheet metal forming. The finite strain combined hardening model discussedhere is integrated by means of the exponential map algorithm in order to fulfil plastic incompressibility.The focus is on different possibilities of evaluating the exponential tensor functions of thematerial model. One option is to use the spectral decomposition to evaluate the exponential tensorfunctions in closed form. Alternatively, the latter functions can be determined by Taylor series expansion.We examine the potential of an explicit formulation of elastoplasticity with combined hardeningwith respect to accuracy and efficiency. The material model equations have been implemented as usermaterial subroutines UMAT and VUMAT for use in the commercial solvers ABAQUS/Standard andABAQUS/Explicit, respectively, where the finite element simulation of draw bending is simulatedboth in implicit and explicit manner.