An energy-momentum conserving algorithm for non-linear hypoelastic constitutive models

Noels, Ludovic; Stainier, Laurent; Ponthot, Jean-Philippe

doi:10.1002/nme.869

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An energy-momentum conserving algorithm for non-linear hypoelastic constitutive models

Noels, Ludovic; Stainier, Laurent; Ponthot, Jean-Philippe

2004 • In International Journal for Numerical Methods in Engineering, 59 (1), p. 83-114

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10.1002/nme.869

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Keywords :

energy-momentum conserving; dynamics; hypoelastic constitutive model; large strain plasticity; finite elements

Abstract :

[en] This paper presents an extension of the energy momentum conserving algorithm, usually developed for hyperelastic constitutive models, to the hypoelastic constitutive models. For such a material no potential can be defined, and thus the conservation of the energy is ensured only if the elastic work of the deformation can be restored by the scheme. We propose a new expression of internal forces at the element level which is shown to verify this property. We also demonstrate that the work of plastic deformation is positive and consistent with the material model. Finally several numerical applications are presented. Copyright (C) 2003 John Wiley Sons, Ltd.

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 for non-linear hypoelastic constitutive models

Publication date :

2004

Journal title :

International Journal for Numerical Methods in Engineering

ISSN :

0029-5981

eISSN :

1097-0207

Publisher :

John Wiley & Sons Ltd, Chichester, United Kingdom

Volume :

Issue :

Pages :

83-114

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://dx.doi.org/10.1002/nme.869

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Available on ORBi :

since 21 July 2008

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Bibliography

Newmark N. A method of computation for structural dynamics. Journal of the Engineering Mechanics Division (ASCE) 1959; 85(EM3):67-94.
Belytschko T, Hughes T. Computational Methods for Transient Analysis. North Holland: Amsterdam, 1983.
Hughes T. The Finite Element Method. Prentice-Hall: Englewood Cliffs, NJ 1987.
Belytschko T, Liu W, Moran B. Nonlinear Finite Elements for Continua and Structures. Wiley: New York, 2000.
Kane C, Mardsen JE, Ortiz M, West M. Variational integrators and the Newmark algorithm for conservative and dissipative mechanical system. International Journal for Numerical Methods in Engineering 2000: 49: 1295-1325.
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.
Simo JC, Tarnow N, Wong KK. Exact energy-momentum conserving algorithms and sympletic schemes for nonlinear dynamics. Computer Methods in Applied Mechanics and Engineering 1992; 100:63-116.
Chung J, Hulbert GJM. A time integration algorithms for structural dynamics with improved numerical dissipations: the generalized-x method. Journal of Applied Mechanics 1993: 60:371-375.
Géradin M, Cardona A. Flexible Multibody Dynamics: A Finite Element Approach. Wiley: New York, 2000.
Ponthot J-P. Traîtement unifié de la mécanique des milieux continus solides en grandes transformations par la méthode des éléments finis. Ph. D. Thesis, Université de Liège, 1995 (in French).
Simo JC, Tarnow N. The discrete energy-momentum method conserving algorithms for nonlinear elastodynamics. Zeitschrift für Angewandte Mathematik and Physik (ZAMP) 1992; 43:757-792.
Simo JC, Gonzalez O. Recent results on the numerical integration of infinite-dimensional hamiltonian system. In: Recent Developments in Finite Element Analysis, Hughes TJR. Onate E. Zienkiewicz OC (eds). CIMNE: Barcelona, Spain, 1994, pp. 255-271.
Simo JC, Tarnow N. A new energy and momentum conserving algorithms for the nonlinear dynamics of shells. International Journal for Numerical Methods in Engineering 1994; 37:2527-2549.
Zhong HG, Crisfield MA. An energy-conserving co-rotational procedure for the dynamics of shell structures. Engineering Computations l998; 15(5):552-576.
Kuhl D, Crisfield MA. Energy-conserving and decaying algorithms in non-linear structural dynamics. International Journal for Numerical Methods in Engineering 1999; 45:569-599.
Sansour C, Wagner W, Wriggers P, Sansour J. An energy-momentum integration scheme and enhanced strain finite elements for non-linear dynamics of shells. International Journal of Nonlinear Mechanics 2002; 37: 951-966.
Brank B. An energy conserving non-linear dynamic finite formulation for flexible composite laminates. Computers and Structures 2002: 80:677-689.
Briseghella L. Majorana C, Pellegrino C. Conservation of angular momentum and energy in the integration of non-linear dynamics equations. Computer Methods in Applied Mechanics and Engineering 1999; 179:247-263.
Laursen T, 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, 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.
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 Enqineering 2001; 191:1639-1675.
Armero F, Petocz 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, Petocz 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.
Laursen T. Computational Contact and Impact Mechanics. Springer: Berlin, 2002.
Armero F, Romero I. Dissipative integration algorithms for nonlinear elastodynamics. In ECCM99. Proceedings of the European Conference on Computational Mechanics. Wunderlich W (ed.). Munich, Germany, 1999, CD-ROM.
Romero I, Armero F. High-frequency dissipative time-stepping algorithms for the dynamics of nonlinear shells. In: ECCOMAS 2000, Proceedings of the Congress on Computational Methods in Applied Sciences and Engineering Oñate E, Brigeda G, Swález B. (eds). Barcelona, Spain, 2000.
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.
Ibrahimbegovic A. Mamouri S. Energy conserving/decaying implicit time-stepping scheme for non-linear dynamics of three-dimensional beams undergoing finite rotations. Computer Methods in Applied Mechanics and Engineering 2002: 191:4241-4258.
Hughes T, Caughey T, Liu W. Finite-element method for non-linear elastodynamics which conserve energy. Journal of Applied Mechanics 1978; 45:366-370.
Kuhl D, Ramm E. Constraint energy momentum algorithm and its application to non-linear dynamics of shells. Computer Methods in Applied Mechanics and Engineering 1996; 136:293-315.
Kuhl D, Ramm E. Generalized energy-momentum method for non-linear adaptive shell dynamics. Computer Methods in Applied Mechanics and Engineering 1999; 178:343-366.
Betsch P, Steinmann P. Inherent energy conserving time finite elements for classical mechanics. Journal of Computational Physics 2000; 160:88-116.
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.
Borri M, Bottasso L. Trainelli L. Integration of elastic multibody system by invariant conserving/dissipating algorithms. i. formulation. Computer Methods in Applied Mechanics and Engineering 2001; 190:3669-3699.
Bottasso L, Borri M, Trainelli L. Integration of elastic multibody system by invariant conserving/dissipating algorithms. ii. numerical schemes and applications. Computer Methods in Applied Mechanics and Engineering 2001; 190:3701-3733.
Nagtegaal J. On the implementation of inelastic constitutive equations with special reference to large deformation problems. Computer Methods in Applied Mechanics and Engineering 1982; 33:469-484.
Nagtegaal J, Veldpaus F. Analysis of metal forming problems with an improved finite strain plasticity formulation. Numerical Methods in Industrial Forming Processes. Pineridge: Swansea, UK, 1982.
Nagtegaal J, Veldpaus F. On the implementation of finite strain plasticity equations in a numerical model. In Numerical Analysis of Forming Processes, Pittman et al. (eds). Wiley: New York, 1984.
Ponthot J-P. Unified stress update algorithms for the numerical simulation of large deformation elasto-plastic and elasto-viscoplastic processes. International Journal of Plasticity 2002; 18:91-126.
Wilkins M. Calculation of elastoplastic flows. In: Methods of Computational Physics. Alder B (ed.). Academic Press; New York, 1964; 211-263.
Maenchen M, Sack S. The tensor code. In Methods of Computational Physics, vol. 3. Alder B (ed.). Academic Press: New York, 1964.
Simo J, Hughes T. Computational Inelasticity. Springer: Berlin, 1998.
Lubliner J. Plasticity, Theory. Macmillan: New York, 1990.
Hilbert H, Hughes T, Taylor R. Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Engineering and Structural Dynamics 1977; 5:283-292.