A Pseudo Flow Theory of Plasticity Based Constitutive Equation for Inverse Analysis Method and its Industry Verification in Sheet Metal Stamping

The Traditional Inverse Analysis Method (TIAM) of sheet metal stamping has the shortcoming of neglecting the effects of deformation history on stress prediction. An Updated Inverse Analysis Method (UIAM) is proposed based on the final workpiece in Euler coordinate system. The UIAM uses the constitutive equation based on pseudo flow theory of plasticity to consider the loading history. In order to avoid numerous iterations to ensure the numerical stability in Newton-Raphson scheme to obtain plastic multiplier ∆λ, the equation in unknown stress vectors is transformed into a scalar equation using the notion of the equivalent stress. Thus a scalar equation of two orders and only one unknown factor ∆λ is obtained. A simple transformation matrix is introduced to reverse this matrix, so that the multiplier ∆λ can be solved explicitly. Results obtained with the TIAM based on deformation theory of plasticity and the updated one based on pseudo flow theory of plasticity are compared with those of the incremental forward finite element solver LS-DYNA. The comparisons of blank configurations and the effective strain distribution show that the proposed plasticity integration algorithm is effective and reliable.