Abstract: Sheet metal flexible-die forming process is the combination of sheet metal deformation and flexible-die deformation. Contact description can be differentiated into two categories, contact between sheet metal and rigid die, and contact between sheet metal and flexible pressure-carrying medium. The penalty function method is used to evaluate the contact force and a finite element formulation and solution algorithm are developed to solve the contact problem between two different type element：Mindlin axisymmetric shell element and solid element. The static-explicit time integration algorithm is employed to limit the incremental step to a size, which will keep the contact state steady. It is illustrated through analyzing the sheet metal deformation by applying the visco-elastoplasticity as flexible pressure-carrying medium that the solution algorithm is valid. The solution algorithm developed can also be used to solve the frictional contact between sheet metal and other type flexible pressure-carrying medium.

Key words: FEM Frictional contact, Sheet metal flexible-die forming, Static explicit algorithm, Defects of material, GTN constitutive, Pre-stretching fracture, Aluminum alloy plate