Novel Plasticity Integration Algorithm in Improved Inverse Analysis Method and its Verification in Clover-Shaped Cup Drawing

An improved inverse analysis method is developed based on the final workpiece in Euler coordinate system. The drawbeads and the radius of the die introduce a complex bending-unbending loading history as the material passes through these regions. Unlike the widespread inverse analysis using deformation theory of plasticity, in order to consider loading history, the improved inverse analysis method uses the constitutive equation based on flow theory of plasticity. In order to avoid numerous iterations to ensure the numerical stability in Newton-Raphson scheme to obtain plastic multiplier Delta lambda, a novel plastic integration algorithm is proposed to consider bending unbending effects. A clover-shaped cup drawing example is numerically simulated with the inverse analysis method based on deformation theory of plasticity and the improved one based on flow theory of plasticity. These simulated results are compared with those of the incremental forward finite element solver LS-DYNA simultaneously. The comparisons of blank configurations and the effective strain distribution show that the proposed plasticity integration algorithm is effective and reliable.