Rigid plastic model of incremental sheet deformation using second‐order cone programming

This paper describes a method for numerically modelling the incremental plastic deformation of shells and applies the method to incremental sheet forming (ISF). An upper bound finite element shell model is developed based on sequential limit analysis under the rigid plastic assumption, which is solved by manipulating the problem into the form of a second‐order cone program (SOCP). Initially, the static upper bound plate problem is investigated and the results are compared with the existing literature. The approach is then extended to a shell formulation using a linearized form of the Ilyushin yield condition and two methods for treating the Ilyushin condition are presented. The model is solved efficiently using SOCP software. The resulting model shows good geometric agreement when validated against an elasto‐plastic model produced using existing commercial software and with measurements from a real product produced using ISF. Copyright © 2008 John Wiley & Sons, Ltd.