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 developed here uses an updated Lagrangian formulation based on incremental nonlinear shell theory which neglects the shear deformation but takes very large displacements and rotations into account. Hill's normally anisotropic yield criterion and associated flow rule are employed. The material is assumed to follow a power law of hardening with strain-rate sensitivity once the initial elastic limit strain is reached. The modified Coulomb law is used to model the interfacial friction. The frictional 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 out-of-plane displacements, resulting in four degrees of freedom at each node. The results from the developed formulation are found to be in good agreement with other numerical solutions and measured data. Applications are made to industry-scale problems using complex tool geometries with multiple curvatures.