energy conserving; momentum conserving; dynamics; variational formulation; elastoplasticity; finite-elements rnethod
Abstract :
[en] In this paper we use the variational formulation of elasto-plastic updates proposed by Ortiz and Stainier (Comput. Methods Appl. Mech. Eng. 1999; 171:419-444) in the context of consistent time integration schemes. We show that such a formulation is well suited to obtain a general expression Of energy momentum conserving algorithms. Moreover, we present numerical examples that illustrate the efficiency of our developments. Copyright (c) 2005 John Wiley
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 :
An energy momentum conserving algorithm using the variational formulation of visco-plastic updates
Publication date :
2006
Journal title :
International Journal for Numerical Methods in Engineering
Newmark N. A method of computation for structural dynamics. Journal of the Engineering Mechanics Division (ASCE) 1959; 85(EM3):67-94.
Belytschko T, Schoeberle DF. On the unconditional stability of an implicit algorithm for non-linear structural dynamics. Journal of Applied Mechanics 1975; 42:865-869.
Hughes TJR. A note on the stability of Newmark's algorithm in nonlinear structural dynamics. International Journal for Numerical Methods in Engineering 1977; 11(2):383-386.
Chung J, Hulbert GJM. A time integration algorithms for structural dynamics with improved numerical dissipations: the generalized-α method. Journal of Applied Mechanics 1993; 60:371-375.
Erlicher S, Bonaventura L, Bursi OS. The analysis of the α-generalized method for non-linear dynamic problems. Computational Mechanics 2002; 28:83-104.
Simo JC, Tarnow N. The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics. Zeitschrift fur Angewandte Mathematik und Physik 1992; 43:757-792.
Laursen TA, Meng X. A new solution procedure for application of energy-conserving algorithms to general constitutive models in nonlinear elastodynamics. Computer Methods in Applied Mechanics and Engineering 2001; 190:6309-6322.
Gonzalez O. Exact energy and momentum conserving algorithms for general models in nonlinear elasticity. Computer Methods in Applied Mechanics and Engineering 2000; 190:1763-1783.
Meng X, Laursen T. Energy consistent algorithms for dynamic finite deformation plasticity. Computer Methods in Applied Mechanics and Engineering 2001; 191:1639-1675.
Meng X, Laursen TA. On energy consistency of large deformation plasticity models, with application to the design of unconditionally stable time integrators. Finite Elements in Analysis and Design 2002; 38:949-963.
Noels L, Stainier L, Ponthot J-P. Energy-momentum conserving algorithm for non-linear hypoelastic constitutive models. International Journal for Numerical Methods in Engineering 2004; 59:83-114.
Noels L, Stainier L, Ponthot J-P. On the use of large time steps with an energy-momentum conserving algorithm for non-linear hypoelastic constitutive models. International Journal of Solids and Structures 2004; 41:663-693.
Sansour C, Wriggers P, Sansour J. On the design of energy-momentum integration schemes for arbitrary continuum formulations. Applications to classical and chaotic motion of shells. International Journal for Numerical Methods in Engineering 2004; 60:2419-2440.
Armero F, Petöcz E. Formulation and analysis of conserving algorithms for frictionless dynamic contact/impact problems. Computer Methods in Applied Mechanics and Engineering 1998; 158:269-300.
Armero F, Petöcz E. A new dissipative time-stepping algorithm for frictional contact problems: formulation and analysis. Computer Methods in Applied Mechanics and Engineering 1999; 179:151-178.
Laursen TA, Chawla V. Design of energy conserving algorithms for frictionless dynamic contact problems. International Journal for Numerical Methods in Engineering 1997; 40:863-886.
Chawla V, Laursen T. Energy consistent algorithms for frictional contact problems. International Journal for Numerical Methods in Engineering 1998; 42:799-827.
Armero F, Romero I. On the formulation of high-frequency dissipative time-stepping algorithms for non-linear dynamics. Part I: low-order methods for two model problems and nonlinear elastodynamics. Computer Methods in Applied Mechanics and Engineering 2001; 190:2603-2649.
Armero F, Romero I. On the formulation of high-frequency dissipative time-stepping algorithms for non-linear dynamics. Part II: second-order methods. Computer Methods in Applied Mechanics and Engineering 2001; 190:6783-6824.
Noels L, Stainier L, Ponthot J-P. Simulation of complex impact problems with implicit time algorithm. Application to a blade-loss problem. International Journal of Impact Engineering, in press.
Betsch P, Steinmann P. Conservation properties of a time FE method. Part I: time-stepping schemes for n-body problems. International Journal for Numerical Methods in Engineering 2000; 49:599-638.
Betsch P, Steinmann P. Conservation properties of a time FE method. Part II: time-stepping schemes for non-linear elastodynamics. International Journal for Numerical Methods in Engineering 2001; 50:1931-1955.
Bauchau OA, Joo T. Computational schemes for non-linear elasto-dynamics. International Journal for Numerical Methods in Engineering 1999; 45:693-719.
Bottasso CL, Borri M. Integrating finite rotation. Computer Methods in Applied Mechanics and Engineering 1998; 164:307-331.
Ortiz M, Stainier L. The variational formulation of viscoplastic updates. Computer Methods in Applied Mechanics and Engineering 1999; 171:419-444.
Radovitzky R, Ortiz M. Error estimation and adaptative meshing in strongly nonlinear dynamics problems. Computer Methods in Applied Mechanics and Engineering 1999; 172:203-240.
Simo JC, Taylor RL. Quasi-incompressible finite elasticity in principal stretches continuum basis and numerical algorithms. Computer Methods in Applied Mechanics and Engineering 1991; 85:273-310.
Antman SA. Nonlinear Problems of Elasticity. Springer: Berlin, 1995.
Fraijs de Veubeke BM. Diffusion des inconnues hyperstatiques dans les voilures à longerons couplés. Bulletins du Service Technique de L'Aéronautique, vol. 24. Imprimerie Marcel Hayez, Bruxelles, Belgium, 1951.
Hu HC. On some variational methods on the theory of elasticity and theory of plasticity. Scientia Sinica 1955; 4:33-54.
Washizu K. On the variational principles of elasticity and plasticity. Technical Report 25-18, Aeroelastic and Structures Research Laboratory, Massachusetts Institute of Technology, Cambridge, USA, 1955.
Felipa CA. On the original publication of the general canonical functional of linear elasticity. Journal of Applied Mechanics 2000; 67(1):217-219.
Crisfield MA. Non-linear Finite Element Analysis of Solids and Structures, vol. 1. Wiley: New York, 2001.
Gonzalez O, Simo JC. On the stability of sympletic and energy-momentum algorithms for non-linear Hamiltonian systems with symmetry. Computer Methods in Applied Mechanics and Engineering 1996; 134:197-222.
Simo JC. Algorithms for static dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Computer Methods in Applied Mechanics and Engineering 1992; 99: 61-112.
Hughes TJR. Stability, convergence and growth and decay of energy of the average acceleration method in nonlinear structural dynamics. Computers and Structures 1976; 6:313-324.
Noels L, Stainier L, Ponthot J-P. Simulation of crashworthiness problems with improved contact algorithms for implicit time integration. International Journal of Impact Engineering, in press.
