Intermediate shapes for incremental sheet forming

Incremental sheet forming has limitations such as when forming a steep wall angle with a small radius tool. These limits need to be anticipated by using a multistage strategy with intermediate shapes, that avoids excessive strains. In designing methods to smooth a formed shape to achieve an intermediate shape, work on digital image processing is informative. In particular, K. Crane [6] and others have used solution of Poisson's diffusion equation to obtain a smoothing of a surface. An alternative approach labelled false elasticity smoothing to estimate intermediate shapes is presented here. Two parameters control smoothing of the final shape: one to scale back curvatures and one to scale back membrane strains. Membrane strains are estimated to give nodal forces. The curvature tensor at any element centre is estimated from the final shape to predict nodal moments. Scaling back moments will reduce local curvature, and scaling back forces will reduce the membrane strains. An elastic finite element solution predicts an intermediate shape, typically giving priority to reducing the local peak curvatures. This can be repeated until the sheet is flattened. The application of this approach to trial geometries is presented, and the choice of smoothing parameters discussed. (paper)