Finite element analysis of the wrinkling initiation and growth in modified Yoshida buckling test

Abstract

Wrinkling is one of the major defects in sheet metal products and may be also attributable to the wear of the tool. The initiation and growth of wrinkles are influenced by many factors such as stress ratios, mechanical properties of the sheet material, geometry of the workpiece, contact condition, etc. In the study, the 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 found by checking the determinent of the stiffness matrix at each iteration and the wrinkling behavior is analyzed by successive iteration with the perturbed guess along the eigenvector. The effect of magnitude of perturbation on the wrinkling behavior can be avoided by the Newton-type iteration method. The finite element formulation is based on the incremental deformation theory and elastic-plastic material modeling. The finite element analysis is carried out using the continuum-based resultant shell elements considering the planar anisotropy of the sheet metal. In order to investigate the effects of geometry and stress state on the wrinkling initiation and growth, a modified Yoshida buckling test is proposed as an effective buckling test. The finite element analysis are carried out for the modified Yoshida buckling test. The buckling behavior of the sheet is analyzed for various modified dimensions.