Wrinkling in sheet metal forming

The wrinkling process in sheet metal forming is analyzed as a bifurcation process of an elastic-plastic thin shell undergoing finite deformation. The wrinkling process is investigated by performing: (a) a finite deformation analysis for determining the bending and membrane behavior of a sheet metal having finite strains, (b) a bifurcation analysis for finding the onset of wrinkling, and (c) a post-bifurcation analysis for tracking the growth or decay of wrinkles. An incremental approach is employed and a convected coordinate system leading to a Lagrangian formulation of the field equations is implemented. Hill's general yield criterion for sheet materials having the normal anisotropy and Hill's quasistatic bifurcation criterion for elastic-plastic solids are applied. A thin shell finite element suitable for sheet metal forming problems which is based on Hill's variational principle and "Quasi-conforming Element Technique" is generated. A general purpose computer program incorporating all the three steps of the overall analysis is developed. Sample problems concerning an unevenly stretched sheet metal and a diagonally stretched square sheet are investigated. The results provide useful knowledge of wrinkling behavior of sheet metals and further analytical data for future references.