Wrinkling criterion for an anisotropic shell with compound curvatures in sheet forming

Wrinkling criteria are proposed for an elastic isotropic and plastic anisotropic shell with compound curvatures in the noncontact region of a sheet subjected to internal forming stresses. A quasi-shallow shell is modeled by Donnell-Mushtari-Vlasov (DMV) shell theory. A bifurcation functional from Hill's general theory of uniqueness and bifurcation in elastic-plastic solids is used to model the local wrinkling phenomenon. Both strain hardening and transverse anisotropy are taken into consideration. This wrinkling criterion is especially useful as a failure criterion in three dimensional finite element modeling (FEM) of sheet forming. Given the principal stresses or strains and the geometry provided at each incremental deformation step, the criterion can be used to predict wrinkles in the elements in the unsupported region.