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

A new implicit approach for the incremental analysis of planar anisotropic elasto-plastic sheet forming processes was developed based on the increment al deformation theory of plasticity. The incremental deformation theory bas ed on minimum work paths enables convenient decoupling of deformation and r otation by the polar decomposition. The mathematical description of a const itutive law for the incremental deformation theory has been previously deri ved from the flow theory along the minimum plastic work path. The resulting incremental constitutive law is frame-indifferent (objective) since the th eory 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 nec king as well as the earing of aluminum alloy sheet samples were simulated f or circular cup drawing and NUMISHEET'93 square cup drawing. The simulated results were compared with experimental results. Simulation was also carrie d out for NUMISHEET'93 front fender in order to show a computational effici ency and robustness, (C) 1999 Elsevier Science Ltd. All rights reserved.