Investigation into wrinkling behavior in the elliptical cup deep drawing process by finite element analysis using bifurcation theory

The initiation and growth of wrinkles in sheet metal forming processes are influenced by many factors such as the stress state, the mechanical properties of the sheet material, the geometry of the body, and the contact conditions. It is difficult to analyze wrinkling initiation and growth considering these factors, because the effects of the factors are very complex and the wrinkling behavior may show a wide variation for small deviation of the factors. In this study, bifurcation theory is introduced for the finite element analysis of wrinkling initiation and growth. All the above mentioned factors are conveniently considered by the finite element method. The wrinkling initiation is determined by checking the determinant of the stiffness matrix at each iteration and the wrinkling behavior is analyzed by successive iteration with the perturbed guess along the eigenvector. The finite element formulation is based on the incremental deformation theory and elastic-plastic material modeling. The finite element analysis is carried out using continuum-based resultant shell elements. The initiation and growth of wrinkling in the elliptical cup deep drawing process are analyzed by the proposed algorithm. The effect of the aspect ratio of a punch on the wrinkling behavior in the elliptical cup deep drawing process is investigated.