An alternative method between implicit and explicit schemes devoted to frictional contact problems in deep drawing simulation

Abstract

Abstract The purpose of this work is to present a family of implicit numerical methods devoted to frictional contact problems in dynamic deep drawing simulations. These methods have been developed to overcome the convergence problems due to strong non-linearities and to simulate spring-back effects. They are based on quasi-Newton solver types. To ensure the convergence of these quasi-Newton methods, time step conditions are required. Then, several convergence criteria are developed to estimate the critical time step and are compared with the stability criteria of the explicit schemes. A relationship between these convergence criteria and the stability one is discussed. The algorithmic performances of these implicit methods are numerically estimated and computational results on a benchmark test sensible to spring-back effects are presented.