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Volume invariant metamorphosis for solid and hollow rolled shape

An alternative approach for the simulation of metal forming process is proposed. The main idea is to simulate the shape change of the material throughout the whole process by metamorphosis, and then analyze the physical property changes among the intermediate shapes. The key advantage of the proposed approach, when compared with FEM, is that less computing power is required. Since in the metal forming process, material is expected to deform permanently, i.e. undergo plastic deformation, the volume of material is invariant over the forming process. Hence, a "three dimensional, volume conserved and parameter controlled" metamorphosis algorithm is developed. The idea is to transform first the object from the spatial domain into another domain, which provides a better control over the volume information. Interpolation is then applied in the new domain and the intermediate shapes are obtained from inverse transformation.