DYNAMIC PLANE-STRAIN FINITE-ELEMENT SIMULATION OF INDUSTRIAL SHEET-METAL FORMING PROCESSES

A plane-strain implicit dynamic finite element formulation is applied for the analysis of sheet-forming processes. The bending model develop ed here uses an updated Lagrangian formulation based on incremental no nlinear shell theory which neglects the shear deformation but takes ve ry large displacements and rotations into account. Hill's normally ani sotropic yield criterion and associated flow rule are employed. The ma terial is assumed to follow a power law of hardening with strain-rate sensitivity once the initial elastic limit strain is reached. The modi fied Coulomb law is used to model the interfacial friction. The fricti onal contact is treated by imposing the constraints directly into the tangent stiffness matrix. The Newton-Raphson algorithm is employed by considering the change in normal due to incremental displacements for contact nodes. Hermite cubic elements are used for the in-plane and ou t-of-plane displacements, resulting in four degrees of freedom at each node. The results from the developed formulation are found to be in g ood agreement with other numerical solutions and measured data. Applic ations are made to industry-scale problems using complex tool geometri es with multiple curvatures.