On inverse form finding for orthotropic plasticity

Abstract

Inverse form finding aims to determine the optimum blank design of a workpiece whereby the desired spatial configuration that is obtained after a forming process, the boundary conditions and the applied loads are known. Inputting the optimal material configuration, a subsequent FEM computation then has to result exactly in the nodal coordinates of the desired deformed workpiece. Germain et al. [1] recently presented a new form finding strategy for isotropic elastoplasticity. Switching between the direct and the inverse mechanical formulation, while fixing the internal plastic variables in the inverse step, uniquely detects the undeformed configuration iteratively. In this contribution, the developed recursive algorithm is extended to anisotropic plasticity. In particular the orthotropic Hill yield function is considered. A load and a displacement-controlled example demonstrate that this new strategy requires only a few iterations to determine the optimal initial design whereby an almost linear convergence rate is obtained.