Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact
It is now well established that discrete energy conservation/dissipation plays a key-role for the unconditional stability of time integration schemes in nonlinear elastodynamics. In this paper, from a rigorous conservation analysis of the Hilber–Hughes–Taylor time integration scheme [H. Hilber, T. H...
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| Veröffentlicht in: | Computer methods in applied mechanics and engineering Jg. 195; H. 37; S. 4890 - 4916 |
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01.07.2006
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| Abstract | It is now well established that discrete energy conservation/dissipation plays a key-role for the unconditional stability of time integration schemes in nonlinear elastodynamics. In this paper, from a rigorous conservation analysis of the Hilber–Hughes–Taylor time integration scheme [H. Hilber, T. Hughes, R. Taylor, Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake Engrg. Struct. Dynam. 5 (1977) 283–292], we propose an original way of introducing a controllable energy dissipation while conserving momenta in conservative strategies like [J. Simo, N. Tarnow, The discrete energy–momentum method: conserving algorithms for nonlinear elastodynamics, Z. Angew. Math. Phys. 43 (1992) 757–792]. Moreover, we extend the technique proposed in [O. Gonzalez, Exact energy and momentum conserving algorithms for general models in nonlinear elasticity, Comput. Methods Appl. Mech. Engrg. 190 (13–14) (2000) 1763–1783] to provide energy-controlling time integration schemes for frictionless contact problems enforcing the standard Kuhn–Tucker conditions at time discretization points. We also extend this technique to viscoelastic models. Numerical tests involving the impact of incompressible elastic or viscoelastic bodies in large deformation are proposed to confirm the theoretical analysis. |
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| AbstractList | It is now well established that discrete energy conservation/dissipation plays a key-role for the unconditional stability of time integration schemes in nonlinear elastodynamics. In this paper, from a rigorous conservation analysis of the Hilber-Hughes-Taylor time integration scheme [H. Hilber, T. Hughes, R. Taylor, Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake Engrg. Struct. Dynam. 5 (1977) 283-292], we propose an original way of introducing a controllable energy dissipation while conserving momenta in conservative strategies like [J. Simo, N. Tarnow, The discrete energy-momentum method: conserving algorithms for nonlinear elastodynamics, Z. Angew. Math. Phys. 43 (1992) 757-792]. Moreover, we extend the technique proposed in [O. Gonzalez, Exact energy and momentum conserving algorithms for general models in nonlinear elasticity, Comput. Methods Appl. Mech. Engrg. 190 (13-14) (2000) 1763-1783] to provide energy-controlling time integration schemes for frictionless contact problems enforcing the standard Kuhn-Tucker conditions at time discretization points. We also extend this technique to viscoelastic models. Numerical tests involving the impact of incompressible elastic or viscoelastic bodies in large deformation are proposed to confirm the theoretical analysis. It is now well established that discrete energy conservation/dissipation plays a key-role for the unconditional stability of time integration schemes in nonlinear elastody-namics. In this paper, from a rigorous conservation analysis of the Hilber-Hughes-Taylor time integration scheme [1], we propose an original way of introducing a controllable energy dissipation while conserving momenta in conservative strategies like [2–5]. Moreover, we extend the technique proposed in [3] to provide energy-controlling time integration schemes for frictionless contact problems enforcing the standard Kuhn-Tucker conditions at time discretization points. We also extend this technique to viscoelastic models. Numerical tests involving the impact of incompressible elastic or viscoelastic bodies in large deformation are proposed to confirm the theoretical analysis. |
| Author | Le Tallec, Patrick Hauret, Patrice |
| Author_xml | – sequence: 1 givenname: Patrice surname: Hauret fullname: Hauret, Patrice email: phauret@aero.caltech.edu organization: Graduate Aeronautical Laboratories, MS 205-45, California Institute of Technology, Pasadena, CA 91125, USA – sequence: 2 givenname: Patrick surname: Le Tallec fullname: Le Tallec, Patrick email: patrick.letallec@polytechnique.fr organization: Laboratoire de Mécanique des Solides, CNRS UMR 7649, Département de Mécanique, Ecole Polytechnique, 91128 Palaiseau Cedex, France |
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| Keywords | Viscoelasticity Time integration schemes Energy–momenta conserving algorithms Energy dissipation 02.60.Jh 46.20 46.30.J Nonlinear elastodynamics Contact Energy method Numerical integration Vibration Low speed Momentum Mechanical contact Frictionless contact Incompressible material Elastic wave Modeling Conservation law Time domain method Non linear elasticity 02.60.Jh; 46.20; 46.30.J Energy conservation Earthquakes Non linear effect Elastodynamics Kuhn Tucker method Time integration schemes; Nonlinear elastodynamics; Energy-momenta conserving algorithms; Energy dissipation; Contact; Viscoelasticity Impact test Structural analysis Mechanical shock Energy-momenta conserving algorithms |
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| SubjectTerms | Computational techniques Contact Energy dissipation Energy–momenta conserving algorithms Engineering Sciences Exact sciences and technology Fundamental areas of phenomenology (including applications) Mathematical methods in physics Mechanical contact (friction...) Mechanics Nonlinear elastodynamics Physics Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Structural mechanics Time integration schemes Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...) Viscoelasticity |
| Title | Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact |
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