Slow-dynamic finite element simulation of manufacturing processes

Explicit time integration and dynamic finite element formulations are increasingly being used to analyze nonlinear static problems in solid and structural mechanics. This is particularly true in the simulation of sheet metal manufacturing processes. Employment of slow-dynamic, quasi-static techniques in static problems can introduce undesirable dynamic effects that originate from the inertia forces of the governing equations. In this paper, techniques and guidelines are presented, analyzed and demonstrated, which enable the minimization of the undesirable dynamic effects. The effect of the duration and functional form of the time histories of the loads and boundary conditions is quantified by the analysis of a linear spring mass oscillator. The resulting guidelines and techniques are successfully demonstrated in the nonlinear finite element simulation of a sheet metal deep drawing operation. The accuracy of the quasi-static, slow-dynamic finite element analyses is evaluated by comparison to results of laboratory experiments and purely static analyses. Various measures that quantify the dynamic effects, including kinetic energy, also are discussed.