Simulation of metal forming processes by volume-conserved metamorphosis

In metal forming, metal is deformed under high stress into a desirable shape. The material will crack if stress is applied in an undesirable magnitude and direction. Finite element analysis can definitely be used here, but this is a time-consuming process and requires intensive computation power. A "three-dimensional, volume conserved and parameter controlled" morphosis algorithm is developed and discussed in the paper. The algorithm suggests an alternate mean for a coarse deformation analysis and is expected to require less computation. The metal forming process is emulated by morphosis and stress values are evaluated only at points with high strain rate. The volume-conserved property provides a pre-requisite to emulate the metal forming process. The deformation trend is then controlled roughly by parameters, so as to provide a better emulation of the forming process. Most popular algorithms used in morphosis rely on the interpolation of corresponding point-pairs, and they are not quite applicable here due to the difficulty in volume control. The proposed algorithm is to first transform the objects before and after the deformation into another domain, which provides a good control of the volume information. Interpolation in the new domain is then carried out. An inverse-transform is then performed to obtain the intermediate shapes in the deformation. The representation of the solid in the new domain is, in fact, a new solid modelling scheme that emphasizes the volume-conservation property of the modelled solid. Efficient transformation between the new scheme and the conventional representation to make the morphosis possible is also discussed.