Efficient implicit FEM simulation of sheet metal forming

Abstract

For the simulation of industrial sheet forming processes, the time discretisation is\ud one of the important factors that determine the accuracy and efficiency of the algorithm. For\ud relatively small models, the implicit time integration method is preferred, because of its inherent\ud equilibrium check. For large models, the computation time becomes prohibitively large and, in\ud practice, often explicit methods are used. In this contribution a strategy is presented that enables\ud the application of implicit finite element simulations for large scale sheet forming analysis.\ud Iterative linear equation solvers are commonly considered unsuitable for shell element models.\ud The condition number of the stiffness matrix is usually very poor and the extreme reduction\ud of CPU time that is obtained in 3D bulk simulations is not reached in sheet forming simulations.\ud Adding mass in an implicit time integration method has a beneficial effect on the condition number.\ud If mass scaling is used—like in explicit methods—iterative linear equation solvers can lead\ud to very efficient implicit time integration methods, without restriction to a critical time step and\ud with control of the equilibrium error in every increment. Time savings of a factor of 10 and more\ud can easily be reached, compared to the use of conventional direct solvers.\ud