A general elasto-plastic finite element formulation based on incremental deformation theory for planar anisotropy and its application to sheet metal forming

Abstract

A new implicit approach for the incremental analysis of planar anisotropic elasto-plastic sheet forming processes was developed based on the incremental deformation theory of plasticity. The incremental deformation theory based on minimum work paths enables convenient decoupling of deformation and rotation by the polar decomposition. The mathematical description of a constitutive law for the incremental deformation theory has been previously derived from the flow theory along the minimum plastic work path. The resulting incremental constitutive law is frame-indifferent (objective) since the theory uses the materially-embedded coordinate system. Utilizing the natural convected coordinate system in the incremental variational formulation, the geometrical evolution of materials and the rotation of planar anisotropic axes were effectively incorporated. Planar anisotropy was represented using a nonquadratic yield function. For verification purposes, the onset of necking as well as the earing of aluminum alloy sheet samples were simulated for circular cup drawing and NUMISHEET'93 square cup drawing. The simulated results were compared with experimental results. Simulation was also carried out for NUMISHEET'93 front fender in order to show a computational efficiency and robustness.