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1 2013

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On inverse form ﬁnding for orthotropic plasticity

Landkammer P., Germain S., Steinmann P.

Computer Assisted Methods in Engineering and Science

2013

Vol. 20, no. 4

337--348

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. 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.