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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Published in:Computer methods in applied mechanics and engineering Vol. 195; no. 37; pp. 4890 - 4916
Main Authors: Hauret, Patrice, Le Tallec, Patrick
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.07.2006
Elsevier
Subjects:
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
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
ISSN:0045-7825, 1879-2138
Online Access:Get full text
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Summary: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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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2005.11.005