[en] Variable step strategies are especially well suited to deal with problems characterized by high non-linearity and contact/impact, and resolved with an implicit scheme. Both phenomena are typical of dynamic simulations of contact-impact problems, as well as sheet metal forming. Constant step size strategies do not give a satisfactory answer for this kind of problem, since it is very difficult, if not impossible, for the user to find an appropriate time step that does not lead to divergence nor generate extremely costly computations. An automatic time stepping algorithm is proposed, which takes into account the recent history of accelerations in the deformable bodies under consideration. More precisely, the adaptation algorithm is based on estimators of the integration error of the differential dynamic balance equations. This allows for adaptation of the step size to capture correctly the transient phenomena, with characteristic times which can range from relatively long (after contact, or during sheet metal forming) to very short (during contact-impact). thus ensuring precision while keeping the computation cost to a minimum. Furthermore, we will see that this strategy can be used in explicit schemes. Additionally, the proposed algorithm automatically takes decisions regarding the necessity of updating the tangent matrix or stopping the iterations, further reducing the computational costs especially, when the Augmented Lagrangian method is used. As an illustration of the capabilities of this algorithm, several numerical simulations (shock absorber devices for vehicle crash-worthiness or sheet metal forming) problems will be presented. Other simulations pertaining to the sheet metal forming for vehicle structures will also be investigated, thus demonstrating the versatility, the capabilities and the efficiency of the proposed strategy.
Disciplines :
Mechanical engineering
Author, co-author :
Noels, Ludovic ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Milieux continus et thermomécanique
Stainier, Laurent ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Milieux continus et thermomécanique
Ponthot, Jean-Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire
Language :
English
Title :
Self-adapting time integration management in crash-worthiness and sheet metal forming computations
Belytschko T., Hughes T. Computational Methods for Transient Analysis, North Holland; 1983.
Benson D.J. (1998) Stable time step estimation for multi-material Eulerian hydrocodes. Computer Methods in Applied Mechanics and Engineering 167:191-205.
Cassano A., Cardona A. (1991) A comparison between three variable-step algorithms for the integration of the equations of motion in structural dynamics. Latin American Research 21:187-197.
Chung J., Hulbert J. (1993) A time integration algorithms for structural dynamics with improved numerical dissipations: The generalized-α method. Journal of Applied Mechanics 60:371-375.
Dutta A., Ramakrishnan C. (1998) Accurate computation of design sensitives for structures under transient dynamic loads using time marching scheme. International Journal for Numerical Methods in Engineering 41:977-999.
Géradin M. Analyse, Simulation et Conception de Systèmes Polyarticulés et Déployables, Cours IPSI, Paris; 1997.
Géradin M., Rixen D. Mechanical Vibrations (Theory and Applications to Structural Dynamics), Masson, Paris; 1994.
Givoli D., Henisberg I. (1993) A simple time-step control scheme. Communications in Numerical Methods in Engineering 9:873-881.
Graillet D. Modélisation tridimensionnelle du contact entre structures à paroies minces dans les phénomènes d'impacts et de Mise à Forme., (To appear); PhD thesis, Université de Liège, Liève, in French; .
Graillet D., Ponthot J.-P. (1999) Efficient implicit schemes for the treatment of the contact between deformable bodies: Applications to shock-absorber devices. IJCrash 4(3):173-286.
Hogge M., Ponthot J.-P. (1996) Efficient implicit schemes for transient problems in metal forming simulation. NUPHYMAT'96, Numerical and Physical Study of Material Forming Processes, CEMEF-Ecole nationale supèrieure des mines de Paris Sophia-Antipolis, France; .
Hughes T. The Finite Element Method, Prentice Hall; 1987.
Hulbert G., Jang I. (1995) Automatic time step control algorithms for structural dynamics. Computer Methods in Applied Mechanics and Engineering 126:155-178.
Laursen T. (1992) Formulation and treatment of frictional contact problems using finite elements., PhD thesis, Department of Mechanical Engineering, Stanford University, USA; .
Noels L. (2000) Détermination automatique de la taille du pas de temps pour les schémas implicites en dynamique non-linéaire (in French). Travail de Fin d'Étude, Université de Liège, Liège; .
Ponthot J.-P. (1995) Traitement unifié de la mécanique des milieux continus solides en grandes transformations par la méthode des éléments finis (in French)., PhD thesis, Université de Liège; .
Ponthot J.-P., Hogge M. (1994) On relative merits of implicit schemes for transient problems in metal forming simulation. International Conference on Numerical Methods for Metal Forming in Industry , International Conference on Numerical Methods for Metal Forming in Industry, Baden-Baden, Germany; 2:128-148.
(1999) User manual of samcef., SAMTECH; Technical Report, Samcef, Liège; 8.