Development of a contact model adapted to incremental forming

Incremental forming is a rather new sheet metal forming process and was developed in response to the observed deficiency in rapid prototyping in this field. It uses a standard smooth-end tool mounted on a numerically controlled multi-axis milling machine. This tool follows a complex tool-path and progressively deforms a clamped sheet into its desired shape. Simulations of incremental forming processes often require very long computation time. Explicit strategy coupled with shell or brick element is one solution; however, the moving contact modeled by a penalty method decreases the accuracy. Penalty methods usually check the contact at nodal points or integration points. This implies that for small tool radii, the size of the shell or the brick elements is strongly limited if a stable tool force representative of the actual process is intended. Indeed, when the element size is too large, the force history becomes dependent on the relative position of the tool and on the points where contact is evaluated, even though the mean deformation energy remains identical to the one computed with the refined mesh. Discontinuous forces modify the stress state in the sheet and in the material behavior when an accurate constitutive law with kinematic hardening is used. This paper presents a new approach that allows one to take into account a contact anywhere inside a small number of elements without using a penalty method.