Formulation of Contact Problems in Sheet Metal Forming Simulation Using Local Interpolation for Tool Surfaces

概要

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The treatment of contact between a sheet and tools is one of the most difficult problems to deal with in finite-element simulations of the sheet metal forming processes. In order to obtain more accurate tool models without increasing the number of elements, this paper describes new techniques for the contact problem using a local interpolation for tool surfaces proposed by Nagata. The Nagata patch enables the creation of tool models that are much more accurate in shape than those of the conventional polyhedral representations. Contact search algorithms between the sheet nodes and the interpolated tool surfaces and a consistent contact tangent stiffness matrix for the sliding sheet nodes were formulated. The proposed contact search algorithms allow robust and accurate contact analyses. The developed algorithms were introduced into the static-explicit elastoplastic finite-element method code STAMP3D. Simulations of a square-cup deep-drawing process with a very coarsely discretized punch model were carried out. The simulated results showed that the proposed algorithms yield the proper deformation process, thus demonstrating the validity of the proposed techniques.