Locking Phenomena in the Use of Solid Elements for Sheet Metal Forming Simulation

This paper is concerned with the use of solid elements in sheet metal forming simulation, particularly springback prediction for flanging when the flanging radii are comparable with the metal thickness. It is demonstrated that appropriate solid elements must be used instead of shell elements in order to obtain adequate results. Numerical difficulties associated with development of suitable solid elements are discussed in detail, with emphasis on the volumetric locking and transverse shear locking phenomena respectively. The transverse shear locking arises from the incompatible deformation modes when the element is used for thin structure bending analysis. A four point bending testing problem is used to study the performances of different solid elements. A locking-free solid element based on assumed strain formulation is developed in Ford in-house program MTLFRM for accurate springback prediction, and a flanging example is given to demonstrate its application.