×

An arbitrary Lagrangian-Eulerian finite element method for large deformation analysis of elastic-viscoplastic solids. (English) Zbl 0825.73687


MSC:

74S05 Finite element methods applied to problems in solid mechanics
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74C20 Large-strain, rate-dependent theories of plasticity
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cheng, J. H.; Kikuchi, N., A mesh rezoning technique for finite element simulations of metal forming processes, Internat. J. Numer. Methods Engrg., 23, 218-228 (1986)
[2] Hirt, C. W.; Amsden, A. A.; Cook, J. L., An arbitrary Lagrangian-Eulerian computing method for all flow speed, J. Comput. Phys., 14, 227-253 (1974) · Zbl 0292.76018
[3] Donea, J.; Fasoli-Stella, P.; Giuliani, S., Lagrangian and Eulerian finite element techniques for transient fluid-structure interaction problems, (Trans. 4th Internat. Conf. on SMIRT, Vol. B (1977)), 1-12
[4] Kennedy, J. M.; Belytschko, T. B., Theory and application of a finite element method for arbitrary Lagrangian-Eulerian and solids, Nucl. Engrg. Des., 68, 129-146 (1981)
[5] Argyris, J.; St. Doltsinis, J.; Fischer, H.; Wustenber, H., Tǵa πǵaνταϱϵι̃, Comput. Methods Appl. Mech. Engrg., 51, 289-362 (1985)
[6] Haber, R. B., A mixed Eulerian-Lagrangian displacement model for large-deformation analysis in solid mechanics, Comput. Methods Appl. Mech. Engrg., 43, 277-292 (1984) · Zbl 0521.73069
[7] Benson, D. J., An efficient, accurate, simple ALE method for nonlinear finite element programs, Comput. Methods Appl. Mech. Engrg., 72, 305-350 (1989) · Zbl 0675.73037
[8] Liu, W. K.; Belytschko, T.; Chang, H., An arbitrary Lagrangian-Eulerian finite element method for path-dependent materials, Comput. Methods Appl. Mech. Engrg., 58, 227-245 (1986) · Zbl 0585.73117
[9] Belytschko, T., An overview of semidiscretization and time integration procedures, (Belytschko, T.; Hughes, T. J.R., Computational Methods for Transient Analysis, Vol. 1 (1983), North-Holland: North-Holland Amsterdam) · Zbl 0542.73106
[10] Cormeau, I., Numerical stability in quasistatic elasto/viscoplasticity, Internat. J. Numer. Methods Engrg., 9, 109-127 (1975) · Zbl 0293.73022
[11] Kumar, V.; Morjaria, M.; Mukherjee, S., Numerical integration of some stiff constitutive models of inelastic deformation, J. Engrg. Math. Tech., 102, 92-96 (1980)
[12] Hughes, T. J.R.; Taylor, R. L., Unconditionally stable algorithms for quasi-static elasto/viscoplastic finite element analysis, Comput. & Structures, 8, 169-173 (1978) · Zbl 0365.73029
[13] Argyris, J. H.; Vaz, L. E.; William, K. J., Integrated finite-element analysis of coupled thermoviscoplastic problems, J. Thermal Stresses, 4, 121-153 (1981)
[14] Ortiz, M.; Popov, E. P., Accuracy and stability of integration algorithms for elastoplastic constitutive relations, Internat. J. Numer. Methods Engrg., 21, 1561-1576 (1985) · Zbl 0585.73057
[15] Belytschko, T.; Mullen, R., Mesh partitions of explicit-implicit time integrations, (U.S.-Germany Symposium on Formulations and Computational Algorithms in Finite Element Analysis (1978), MIT Press: MIT Press Cambridge, MA) · Zbl 0434.73074
[16] Perzyna, P., Fundamental problems in viscoplasticity, Adv. Appl. Mech., 9, 243-377 (1966)
[17] Ghosh, S.; Kikuchi, N., Finite element formulation for the simulation of hot sheet metal forming processes, Internat. J. Engrg. Sci., 26, 2, 143-161 (1988) · Zbl 0631.73038
[18] Wilkins, M. L., Calculation of elastic-plastic flow, (Adler, B.; etal., Methods of Computational Physics, Vol. 3 (1964), Academic Press: Academic Press New York)
[19] Krieg, R. D.; Krieg, D. B., Accuracies of numerical solution methods for the elastic-perfectly plastic model, ASME J. Pressure Vessel Tech., 99, 510-515 (1977)
[20] Ortiz, M.; Pinsky, P. M.; Taylor, R. L., Operator split method for the numerical solution of the elastoplastic dynamic problem, Comput. Methods Appl. Mech. Engrg., 39, 137-157 (1983) · Zbl 0501.73077
[21] Rice, J. R.; Tracey, D. M., Computational fracture mechanics, (Fenves, S. J., Proc. Symp. Numerical Methods in Structural Mechanics (1973), Academic Press: Academic Press New York), 585
[22] Ortiz, M.; Simo, J. C., An analysis of a new class of integration algorithms for elasto-plastic constitutive relations, Internat. J. Numer. Methods Engrg., 23, 353-366 (1986) · Zbl 0585.73058
[23] Green, A. E.; Naghdi, P. M., A general theory of an elastic-plastic continuum, Arch. Rat. Mech. Anal., 18, 251-281 (1965) · Zbl 0133.17701
[24] Green, A. E.; McInnis, B. C., Generalized hypo-elasticity, (Proc. Roy. Soc. Edinburgh, A57 (1967)), 220 · Zbl 0149.43201
[25] Dienes, J. K., On the analysis of rotation and stress in deforming bodies, Acta Mech., 32, 217 (1979) · Zbl 0414.73005
[26] Johnson, G. C.; Bammann, D. J., A discussion of stress rates in finite deformation problems, Sandia Report, SAND 82-8821 (1982)
[27] Eftis, J.; Jones, D. L., Evaluation and development of constitutive relations for inelastic behavior, (Technical Report (1983), Air Force Office of Scientific Research: Air Force Office of Scientific Research Washington DC)
[28] Hughes, T. J.R., Unconditionally stable algorithms for nonlinear heat conduction, Comput. Methods Appl. Mech. Engrg., 10, 135-139 (1977)
[29] Hughes, T. J.R.; Belytschko, T., A precis of developments in computational methods for transient analysis, J. Appl. Mech., 50, 1033-1041 (1983) · Zbl 0533.73002
[30] Hughes, T. J.R., Analysis of transient algorithms with particular reference to stability behaviour, (Belytschko, T.; Hughes, T. J.R., Computational Methods for Transient Analysis, Vol. 1 (1983), North-Holland: North-Holland Amsterdam) · Zbl 0459.73069
[31] Hughes, T. J.R.; Winget, J., Finite rotation effects in numerical integration of rate constitutive arising in large-deformation analysis, Internat. J. Numer. Methods Engrg., 15, 12, 1862-1867 (1980) · Zbl 0463.73081
[32] Kikuchi, N.; Oden, J. T., Contact problems in elastostatics, (Oden, J. T.; Carey, G. F., Finite Elements; Special Problems in Solid Mechanics, Vol. V (1984), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ) · Zbl 0685.73002
[33] Kikuchi, N.; Song, Y. J., Penalty/finite element approximations of a class of unilateral problems in linear elasticity, Quart. Appl. Math., XXXIX, 1-22 (1981) · Zbl 0457.73097
[34] Pinsky, P. M.; Ortiz, M.; Pister, K. S., Numerical integration of rate constitutive equations in finite deformation analysis, Comput. Methods Appl. Mech. Engrg., 40, 137-158 (1983) · Zbl 0504.73057
[35] Hughes, T. J.R., Numerical implementation of constitutive models: rate-independent deviatoric plasticity, (Nemat-Nasser, S.; Asaro, R. J.; Hegemier, G. A., Theoretical Foundations for Large Computations of Nonlinear Behavior (1984), Martinus Nijhoff: Martinus Nijhoff Dordrecht)
[36] Bathe, K. J.; Cimento, A. P., Some practical procedures for the solution of nonlinear finite element equations, Comput. Methods Appl. Mech. Engrg., 22, 59-85 (1980) · Zbl 0435.73080
[37] Matthies, H.; Strang, G., The solution of nonlinear finite element equations, Internat. J. Numer. Methods Engrg., 14, 11, 1613-1626 (1979) · Zbl 0419.65070
[38] Walker, H. F., Numerical solutions of nonlinear equation, University of California, Lawrence Livermore National Laboratory, Rept. UCID-18285 (1979)
[39] J.O. Hallquist, Nike 2D: An implicit, finite deformation, finite element code for analyzing the static and dynamic response of two-dimensional solids, University of California, Lawrence Livermore Laboratory, Rept. UCRL-52678.; J.O. Hallquist, Nike 2D: An implicit, finite deformation, finite element code for analyzing the static and dynamic response of two-dimensional solids, University of California, Lawrence Livermore Laboratory, Rept. UCRL-52678.
[40] Hughes, T. J.R., Generalization of selective integration procedures to anisotropic and nonlinear media, Internat. J. Numer. Methods Engrg., 15, 1413-1418 (1980) · Zbl 0437.73053
[41] Belytschko, T.; Bachrach, W. E., Simple quadrilaterals with high coarse mesh accuracy, AMD-73, 39-56 (1985) · Zbl 0623.73074
[42] Koh, B. C.; Kikuchi, N., New improved hourglass control for bilinear and trilinear elements in anisotropic linear elasticity, Comput. Methods Appl. Mech. Engrg., 65, 1-46 (1987) · Zbl 0621.73104
[43] Owen, D. R.J.; Hinton, E., Finite elements in Plasticity; Theory and practice (1980), Pineridge: Pineridge Swansea · Zbl 0482.73051
[44] Key, S. W., (Nemat-Nasser, S.; Asaro, R. J.; Hegemier, G. A., On an implementation of finite strain plasticity in transient dynamic large-deformation calculations (1984), Martinus Nijhoff: Martinus Nijhoff Dordrecht)
[45] Dumas, G.; Baronet, C. N., Elastoplastic indentation of a half-space by an infinitely long rigid circular cylinder, Internat. J. Mech. Sci., 13, 519-530 (1971)
[46] Gelten, C. J.M.; Konter, A. W.A., Application of mesh rezoning in the updated Lagrangian method to metal forming analyses, (Pittman, J. F.T.; Wood, R. D.; Alexander, J. M.; Zienkiewicz, O. C., Numerical Methods in Industrial Forming Processes (1982), Pineridge: Pineridge Swansea)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.