Research On One Step Inverse Forming FEM And Crash Simulation Of Auto Body Part

During the automotive design and manufacture period, it is the main factor of auto product development speed and quality that the design and manufacture level of the auto body die especially auto panel die. The one step inverse forming finite element method based on deformation theory will became a quickly formability evaluation tool and it is applied suitably in part and die design phase. The research contents of this paper are the one step inverse forming FEM of auto body part and applications in the blank sheet prediction of flange forming, the spring back simulation of bend forming and the crash simulation with forming effects. The research works are supported by the key project of National Natural Science Funds "The basic theory, calculation method and key technique of stamping and die design" (19832020) and the key project of National Outstanding Scientific Youth Funds "The CAD expert system theory of stamping design based on KBE and the research on the polymer forming theory and calculation method" (10125208).The main assumption adopted by the one step inverse forming FEM is the proportional loading assumption. It only considers the initial and the final state without considering the medium state. The basic idea of this method is that we look for the nodal positions in the initial flat blank from the final part, and then the distribution of strain, stress and thickness in the final configuration can be calculated by comparing the nodal position in the initial flat sheet with the one of the final part. Using a generalized Kirchhoff assumption, the initial and the final position vectors of a material point q can be expressed with respect to point p on the mid-surface of C. The inverse Cauchy-Green left tensor can be obtained by with (1)The inverse Cauchy-Green left tensor can be obtained by (2)The eigenvalue calculation of [B]-1 gives two principal plane stretches λ1, λ2 and their direction transformation matrix [M]. Then, the thickness stretch λ3 is calculated by the incompressibility assumption. Finally, the logarithmic strains are obtained (3)The elastic-plastic deformation is assumed to be independent on the loading path and a total constitutive law is obtained. (4)Where and are the total equivalent strain and the equivalent stress. The mean planar isotropic coefficient r is obtained from the three anisotropic coefficients: r = (r0 + 2r45 + r90)/4.The inverse forming FEM cannot deal with contact problems depending on the loading history, so the tool actions (punch, die and drawbead) are simply represented by some external forces at the final configuration. Then, a non-linear equilibrium system can be obtained. (5)This non-linear equilibrium system can be calculated by the Newton-Raphson iterative method. (6) Where ω is the relaxation factor and [KT(ui)] is the tangent stiffness matrix in the i iterative step.The initial solution of one step inverse forming FEM for Newton-Raphson iteration is calculated by the initial solution predictive algorithm based on linear elastic reverse deformation. The basic idea is that we assume the initial flat blank translate into the final part by linear elastic reverse deformation neglecting all of external load. Then the equilibrium equations are established by the linear elastic FEM in the initial flat blank. The nodal residual force vector in the initial flat blank will satisfy the initial convergence conditions by iterative calculation. Finally we can get the initial solution.The one step inverse forming FEM must consider the curve binder effect for the complicated auto panel with curve binder. The one step inverse forming FEM with curve binder has two steps. The first step is from the final part to the given curve binder surface, which is named medium configuration. The second step is from the curve binder to the initial flat blank. The projection algorithm of the curve binder is t...