Numerical formulations and algorithms for solving contact problems in metal forming simulation

The problem of contact between a part and a tool or between two deforming bodies is analysed in view of metal-forming processes. For simplicity, only the case of viscoplastic materials is considered. The velocity formulation is presented. The contact with a rigid tool is considered "rst and various forms of contact formulations are described: nodal contact, integral or discrete formulation with a penalty or with a Lagrange multiplier method. The time integration is considered which results in various explicit or implicit contact formulations. A special attention is paid to the contact between two deforming bodies or to the self-contact when a fold is generated in the work-piece. Some 2-D and 3-D application examples illustrate the e!ectiveness of the proposed formulations and algorithms