Elasto-plastic explicit FE formulation and parallelization using an adaptive refinement scheme for sheet metal forming

Abstract

The forming processes to make the work-piece of sheet metal deformed to the useful shape by inducing plastic deformation are called stamping, press working or sheet metal forming process. The sheet metal forming problems in engineering are in general associated with complex geometries, contact, large deformations, etc. In order to make the sheet metal forming simulation applied in engineering, therefore, the improvement of simulation accuracy and efficiency should be achieved. In the present study, the elasto-plastic explicit finite element formulation is developed with adaptive refinement scheme and parallelization for economic computation. An accuracy improvement in sheet metal forming analysis is achieved by adopting a simplified scheme for considering the transverse normal stresses of the sheet metal, which are induced by contact during the forming procedure. Shell element is generally formulated based on the plane stress condition. In sheet metal forming processes, however, a blank undergoes large deformation and rotation due to the contact with tools, as it is formed into a complicated shape and as such, it may be in a stress state that cannot be well expressed by the plane stress condition. To this end, a new algorithm has been proposed which considers transverse normal stress without any reformulation of shell elements in the analysis of sheet metal forming processes. The proposed algorithm is applicable to any yield criterion, return mapping method, hardening law and any shell or membrane elements. Through several numerical examples, it has been demonstrated that the proposed algorithm has almost the same accuracy as the static implicit finite element code, ABAQUS using continuum elements and almost the same efficiency as conventional dynamic explicit FEM using shell elements. Also, the error indicator and following refinement scheme that are suitable to the sheet metal forming analysis is tested and applied to the industrial problems. Generally, 3-dim...