| Two finite element formulations, suitable for sheet metal forming simulation, are proposed. The LNQS formulation features a linear and quadratic through thickness variation of the normal and shear strain, respectively. The CNQS formulation features a cubic and quadratic through thickness variation of the normal and shear stain, respectively. The LNQS model exhibits the ability to deform without the consequences of shear, Poisson's or volume locking, while the CNQS model has been shown to exhibit some locking mechanisms due to an inconsistent shear strain field. The proposed elements exactly satisfy the shear strain (and stress) at the top and bottom of the element. These features, therefore, help qualify the elements to be used in sheet metal simulation procedures where shear strain is appreciable in the through-thickness direction. The LNQS in-plane strain due to both bending and membrane effects is accurately captured for plane strain metal forming cases with and without friction. A system of evaluating and validating the elements, which involves the introduction of a FORTRAN subroutine within a commercial finite element software main program, has been established. In general, good correlation is found among the proposed model solutions and those found in literature. |
