Volume-preserving energy-momentum schemes for isochoric multiplicative plasticity

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 41-44, 2007, Pages 4130-4159

  Armero, F ^a   Zambrana Rojas, C ^a  

^a Department of Civil and Environmental Engineering ^*  (United States)

Author keywords

Energy momentum schemes; Finite strain multiplicative plasticity; Nonlinear dynamics; Return mapping algorithms; Time stepping algorithms

Indexed keywords

ALGORITHMS; ANGULAR MOMENTUM; COMPUTER SIMULATION; DYNAMICS; ENERGY DISSIPATION; EQUATIONS OF MOTION; PLASTIC DEFORMATION; STRAIN;

ENERGY-MOMENTUM SCHEMES; FINITE STRAIN MULTIPLICATIVE PLASTICITY; RETURN MAPPING ALGORITHMS; TIME-STEPPING ALGORITHMS;

PLASTICITY;

ALGORITHMS; ANGULAR MOMENTUM; COMPUTER SIMULATION; DYNAMICS; ENERGY DISSIPATION; EQUATIONS OF MOTION; PLASTIC DEFORMATION; PLASTICITY; STRAIN;

EID: 34547601985     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.04.002     Document Type: Article

References (37)

1. Armero F. On the locking and stability of finite elements in finite deformation plane strain problems. Comput. Struct. 75 (2000) 261-290
2. Armero F. Energy-dissipative momentum-conserving time-stepping algorithms for finite strain multiplicative plasticity. Comput. Methods Appl. Mech. Engrg. 195 (2006) 4862-4889
3. F. Armero, Assumed strain finite element methods for conserving temporal integrations in nonlinear solid dynamics, Technical Report UCB/SEMM-2006/01, UC Berkeley, 2006, submitted for publication.
4. Armero F., and Love E. An arbitrary Lagrangian-Eulerian finite element method for finite strain plasticity. Int. J. Numer. Methods Engrg. 57 (2003) 471-508
5. Armero F., and Romero I. On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part I: Low order methods for two model problems and nonlinear elastodynamics. Comput. Methods Appl. Mech. Engrg. 190 (2001) 2603-2649
6. Armero F., and Romero I. On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part II: High order methods. Comput. Methods Appl. Mech. Engrg. 190 (2001) 6783-6824
7. Crisfield M., and Shi J. A co-rotational element/time-integration strategy for non-linear dynamics. Int. J. Numer. Methods Engrg. 37 (1994) 1897-1913
8. Cuitinho A.M., and Ortiz M. A material independent method for extending stress update algorithms form small strain plasticity to finite plasticity with multiplicative kinematics. Engrg. Comput. 17 (1992) 437-451
9. Eterovich A.L., and Bathe K.J. A hyperelastic based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using logarithmic stresses and strain measures. Int. J. Numer. Methods Engrg. 30 (1990) 1099-1115
10. Géradin M., and Cardona A. Flexible Multibody Dynamics (2001), John Wiley & Sons, Chichester
11. González O. Exact energy-momentum conserving algorithms for general models in nonlinear elasticity. Comput. Methods Appl. Mech. Engrg. 190 (2000) 1763-1783
12. Hughes T.J.R. The Finite Element Method (1987), Prentice-Hall, Englewood Cliffs
13. Kane C., Marsden J.E., Ortiz M., and West M. Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems. Int. J. Numer. Methods Engrg. 49 (2000) 1295-1325
14. Kuhl D., and Crisfield M.A. Energy conserving and decaying algorithms in non-linear structural dynamics. Int. J. Numer. Methods Engrg. 45 (1997) 569-599
15. Kuhl D., and Ramm E. Constraint energy momentum algorithm and its application to non-linear dynamics of shells. Comput. Methods Appl. Mech. Engrg. 136 (1996) 293-315
16. Lee E.H., and Liu D.T. Finite strain elastic-plastic theory particularly for plane wave analysis. J. Appl. Phys. 38 (1967)
17. Lee E.H. Elastic-plastic deformation at finite strains. J. Appl. Mech. 36 (1969) 1-6
18. Marsden J.E., and Hughes T.J.R. Mathematical Foundations of Elasticity (1983), Prentice-Hall, Englewood Cliffs
19. Meng X.N., and Laursen T.A. Energy consistent algorithms for dynamic finite deformation plasticity. Comput. Methods Appl. Mech. Engrg. 191 (2002) 1639-1675
20. Miehe C. Exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals. Int. J. Numer. Methods Engrg. 39 (1996) 3367-3390
21. Moler C., and van Loan C. Nineteen dubious ways to compute the exponential of a matrix. SIAM Rev. 20 (1978) 801-836
22. Nagtegaal J.C., Parks D.M., and Rice J.R. On numerically accurate finite element solutions in the fully plastic range. Comput. Methods Appl. Mech. Engrg. 4 (1974) 153-177
23. Newmark N.M. A method of computation for structural dynamics. ASCE J. Engrg. Mech. 85 (1959) 67-94
24. Noels L., Stainier L., and Ponthot J.P. An energy-momentum conserving algorithm for non-linear hypoelastic constitutive models. Int. J. Numer. Methods Engrg. 59 (2004) 83-114
25. Ogden R.W. Non-Linear Elastic Deformations (1984), Ellis-Harwood, Chichester
26. Schröder J., Gruttmann F., and Löblein J. A simple orthotropic finite elasto-plasticity model based on generalized stress-strain measures. Comput. Mech. 30 (2002) 48-64
27. Shoemake K. Animating rotations with quaternion curves. Proceedings of the 12th Annual International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH'85 vol. 19 (1985), ACM 245-254
28. Simo J.C. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Comput. Methods Appl. Mech. Engrg. 90 (1992) 61-112
29. Simo J.C. Numerical Analysis of Classical Plasticity. In: Ciarlet P.G., and Lions J.J. (Eds). Handbook for Numerical Analysis vol. IV (1998), Elsevier, Amsterdam
30. Simo J.C., and Tarnow N. The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics. ZAMP 43 (1992) 757-793
31. Simo J.C., Taylor R.L., and Pister K. Variational and projection methods for the volume constraint in finite deformation elastoplasticity. Comput. Methods Appl. Mech. Engrg. 57 (1988) 177-208
32. Spurrier R.A. Comment on 'singularity-free extraction of a quaternion from direction cosine matrix'. J. Spacecraft 15 (1978) 255
33. Taylor G.I. The use of flat-ended projectiles for determining dynamic yield stress i. theoretical considerations. Proc. Roy. Soc. Ser. A 194 (1948) 289-299
34. Truesdell C., and Toupin R.A. The classical field theories. In: Flügge S. (Ed). Handbuch der Physik vol. III/1 (1960), Springer-Verlag, Berlin
35. Wehage R. Quaternions and Euler parameters: a brief exposition. In: Haug E. (Ed). Computer Aided Analysis and Optimization of Mechanical System Dynamics (1984), Springer-Verlag
36. Weber G., and Anand L. Finite deformation constitutive equations and time integration procedure for isotropic hyperelastic-viscoelastic solids. Comput. Methods Appl. Mech. Engrg. 79 (1990) 173-202
37. Wilkins M.L., and Guinan M.W. Impact of cylinders on a rigid boundary. J. Appl. Phys. 44 (1973) 1200-1206