Frictional contact problems in sectional finite element analysis of sheet metal flexible-die forming process

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, while finite element formulation and solution algorithm are developed to solve the contact problem between 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.