The objective of this investigation is to develop a nonlinear finite element formulation for the elastic-plastic analysis of flexible multibody systems. The Lagrangian plasticity theory based on flow theory is used to account for the effect of plasticity in flexible multibody dynamics. It is demonstrated that the principle of objectivity that is an issue when existing finite element formulations using rate-type constitutive equations are used is automatically satisfied when the stress and strain rate are directly calculated in the Lagrangian descriptions using the absolute nodal coordinate formulation employed in this investigation. This is attributed to the fact that, in the finite element absolute nodal coordinate formulation, the position vector gradients can completely define the state of rotation and deformation within the element. As a consequence, the numerical algorithm used to determine the plastic deformations such as the radial return algorithm becomes much simpler when the absolute nodal coordinate formulation is used as compared to existing finite element formulations that employ incrementally objective algorithms. Several numerical examples are presented in order to demonstrate the use of the formulations presented in the paper.
Issue Section:
Technical Papers
1.
Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd, Cambridge University Press.
2.
Ambro´sio
, J. A. C.
, and Nikravesh
, P. E.
, 1992
, “Elasto-Plastic Deformations in Multibody Dynamics
,” Nonlinear Dyn.
, 3
, pp. 85
–104
.3.
Gerstmayr, J., and Irschik, H., 2002, “Computational Methods for Elasto-Plastic Multibody Dynamic Systems,” Proceedings of Fifth World Congress on Computational Mechanics, Vienna, Austria.
4.
Gerstmayr
, J.
, Holl
, H. J.
, and Irschik
, H.
, 2001
, “Development of Plasticity and Damage in Vibrating Structural Elements Performing Guided Rigid-Body Motions
,” Arch. Appl. Mech.
, 71
, pp. 135
–145
.5.
Hill, R., 1950, The Mathematical Theory of Plasticity, Clarendon Press.
6.
Naghdi
, P. M.
, 1990
, “A Critical Review of the State of Finite Plasticity
,” Journal of Applied Mathematics and Physics (ZAMP)
, 41
, pp. 315
–394
.7.
Lee
, E. H.
, and Liu
, D. T.
, 1967
, “Finite Strain Elastic-Plastic Theory Particularly for Plane Wave Analysis
,” J. Appl. Phys.
, 38
, pp. 19
–27
.8.
Lee
, E. H.
, 1969
, “Elastic-Plastic Deformation at Finite Strains
,” ASME J. Appl. Mech.
, 36
, pp. 1
–6
.9.
Johnson
, G. C.
, and Bammann
, D. J.
, 1984
, “Discussion of Stress Rates in Finite Deformation Problems
,” Int. J. Solids Struct.
, 20
, pp. 725
–737
.10.
Khan, A. S., and Huang, S., 1995, Continuum Theory of Plasticity, Wiley.
11.
Nagtegaal, J. C., and De Jong, J. E., 1982, “Some Aspects of Non-Isotropic Work Hardening in Finite Strain Plasticity,” Plasticity of Metal at Finite Strain, Stanford University Press, pp. 65–102.
12.
Green
, A. E.
, and Naghdi
, P. M.
, 1965
, “A General Theory of Elasto-Plastic Continuum
,” Arch. Ration. Mech. Anal.
, 18
, pp. 221
–281
.13.
Green
, A. E.
, and Naghdi
, P. M.
, 1971
, “Some Remarks on Elastic-Plastic Deformation at Finite Strain
,” Int. J. Eng. Sci.
, 9
, pp. 1219
–1229
.14.
Lee
, E. H.
, 1981
, “Some Comments on Elastic-Plastic Analysis
,” Int. J. Solids Struct.
, 17
, pp. 859
–872
.15.
Nemat-Nasser
, S.
, 1982
, “On Finite Deformation Elasto-Plasticity
,” Int. J. Solids Struct.
, 18
, pp. 857
–872
.16.
Nagtegaal
, J. C.
, 1982
, “On the Implementation of Inelastic Constitutive Equations with Special Reference to Large Deformation Problems
,” Comput. Methods Appl. Mech. Eng.
, 33
, pp. 469
–484
.17.
Simo
, J. C.
, 1988
, “A Framework for Finite Strain Elastoplasticity Based on Maximum Plastic Dissipation and the Multiplicative Decomposition: Part I Continuum Formulation
,” Comput. Methods Appl. Mech. Eng.
, 66
, pp. 199
–219
.18.
Simo, J. C., and Hughes, T. J. R., 1998, Computational Inelasticity, Springer.
19.
Simo
, J. C.
, 1992
, “Algorithms for Static and Dynamic Multiplicative Plasticity That Preserve the Classical Return Mapping Schemes of the Infinitesimal Theory
,” Comput. Methods Appl. Mech. Eng.
, 99
, pp. 61
–112
.20.
Crisfield, M. A., 1996, Non-Linear Finite Element Analysis of Solids and Structures, Volume 2, Wiley.
21.
Eterovic
, A. L.
, and Bathe
, K. J.
, 1990
, “A Hyperelastic-Based Large Strain Elastoplastic Constitutive Formulation with Combined Isotropic-Kinematic Hardening Using the Logarithmic Stress and Strain Measures
,” Int. J. Numer. Methods Eng.
, 30
, pp. 1099
–1114
.22.
Weber
, G.
, and Anand
, L.
, 1990
, “Finite Deformation Constitutive-Equations and a Time Integration Procedure for Isotropic, Hyperelastic Viscoplastic Solids
,” Comput. Methods Appl. Mech. Eng.
, 79
, pp. 173
–202
.23.
Papadopoulos
, P.
, and Lu
, J.
, 1998
, “A General Framework for the Numerical Solution of Problems in Finite Elasto-Plasticity
,” Comput. Methods Appl. Mech. Eng.
, 159
, pp. 1
–18
.24.
Meng
, X. N.
, and Laursen
, T. A.
, 2002
, “Energy Consistent Algorithms for Dynamic Finite Deformation Plasticity
,” Comput. Methods Appl. Mech. Eng.
, 191
, pp. 1639
–1675
.25.
Shabana
, A. A.
, and Yakoub
, R. Y.
, 2001
, “Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements
,” ASME J. Mech. Des.
, 123
, pp. 606
–621
.26.
Mikkola
, A. M.
, and Shabana
, A. A.
, 2003
, “A Non-Incremental Finite Element Procedure for the Analysis of Large Deformation of Plates and Shells in Mechanical System Applications
,” Multibody System Dynamics
, 9
, pp. 283
–309
.27.
Shabana
, A. A.
, and Mikkola
, A. M.
, 2003
, “Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity
,” ASME J. Mech. Des.
, 125
, pp. 342
–350
.28.
Sugiyama
, H.
, Escalona
, J. L.
, and Shabana
, A. A.
, 2003
, “Formulation of Three-Dimensional Joint Constraints Using the Absolute Nodal Coordinates
,” Nonlinear Dyn.
, 31
, pp. 167
–195
.29.
Bonet, J., and Wood, R. D., 1997, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press.
30.
Wilkins, M. L., 1964, “Calculation of Elasto-Plastic Flow,” Methods of Computational Physics 3, Academic Press.
31.
Krieg, R. D., and Key, S. W., 1976, “Implementation of a Time Dependent Plasticity Theory into Structural Computer Programs,” Constitutive Equations in Viscoplasticity: Computational and Engineering Aspects, AMD-20, ASME.
32.
Simo
, J. C.
, Taylor
, R. L.
, and Pister
, K. S.
, 1985
, “Variational and Projection Methods for the Volume Constraint in Finite Deformation Elasto-Plasticity
,” Comput. Methods Appl. Mech. Eng.
, 51
, pp. 177
–208
.33.
Yakoub
, R. Y.
, and Shabana
, A. A.
, 1999
, “Use of Cholesky Coordinates and the Absolute Nodal Coordinate Formulation in the Computer Simulation of Flexible Multibody Systems
,” Nonlinear Dyn.
, 20
, pp. 267
–282
.34.
Simo
, J. C.
, and Taylor
, R. L.
, 1985
, “Consistent Tangent Operators for Rate-Independent Elastoplasticity
,” Comput. Methods Appl. Mech. Eng.
, 48
, pp. 101
–118
.35.
ANSYS Theory Reference 6.1, 2002, SAS IP, Inc.
36.
Simo
, J. C.
, and Vu-Quoc
, L.
, 1986
, “Three-Dimensional Finite-Strain Rod Model. Part II: Computational Aspects
,” Comput. Methods Appl. Mech. Eng.
, 58
, pp. 79
–116
.37.
Campanelli
, M.
, Berzeri
, M.
, and Shabana
, A. A.
, 2000
, “Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems
,” ASME J. Mech. Des.
, 122
, pp. 498
–507
.Copyright © 2004
by ASME
You do not currently have access to this content.
