Numerical assessment of springback for the deep drawing process by level set interpolation using shape manifolds

In this paper, we introduce an original shape representation approach for post-springback characterization based on the automatic generation of parameterized level set functions. The central idea is the concept of the shape manifold representing the design domain in the reduced-order shape-space. Performing Proper Orthogonal Decomposition on the shapes followed by using the Diffuse Approximation allows us to efficiently reduce the problem dimensionality and to interpolate uniquely between admissible input shapes, while also determining the smallest number of parameters needed to characterize the final formed shape. We apply this methodology to the problem of springback assessment for the deep drawing operation of metal sheets.