Second order cone programming in modeling incremental deformation

Incremental sheet forming (ISF) is a flexible method for forming sheet metal that can be considered as an incremental deformation process. It is applicable to low volume parts manufacturing and rapid prototyping. Existing models for ISF, which are predominantly based on standard finite element analysis software, are extremely slow and therefore not suitable for control engineering purposes. A fast method for modeling deformation in ISF is required that can form the basis of a model predictive control system to regulate the geometric accuracy of parts produced by the process. This paper proposes a model that is based on the numerical minimization of plastic energy within the material. By using a quadratic yield function to describe the yield surface, the minimization can be formulated as a Second Order Cone Programming (SOCP) optimization problem. This model is solved efficiently by the use of primal dual interior point SOCP algorithms.