×

Line-search methods in general return mapping algorithms with application to porous plasticity. (English) Zbl 1163.74047

Summary: The paper focuses on the application of line-search methods in general return mapping algorithms. Two inexact line-search methods and an exact line-search method are investigated regarding their convergence properties within an automatic time incrementation in finite element calculations. As an example for the assessment of the algorithms, an elastic-plastic and an elastic-viscoplastic version of Gurson’s porous plasticity model are used in simulations of the necking of a tensile bar. It is shown that larger time increments are possible and, therefore, a smaller number of increments are required when using line-search methods. The exact line-search method shows the best performance concerning the required number of increments, but takes more CPU time to complete the simulation. The application of the inexact line search methods in general lowers the number of increments along with a reduction in CPU time, as compared with the case when no line-search is used.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)

Software:

ABAQUS
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Gurson, Journal of Engineering Materials and Technology 99 pp 2– (1977) · doi:10.1115/1.3443401
[2] Numerical implementation of constitutive models: rate independent deviatoric plasticity. In Theoretical Foundation for Large-scale Computations of Nonlinear Material Behavior, , (eds). Martinus Nijhoff Publishers: Dordrecht, Boston, Lancaster, 1984.
[3] Ortiz, International Journal for Numerical Methods in Engineering 21 pp 1561– (1985)
[4] Zhang, Computer Methods in Applied Mechanics and Engineering 121 pp 15– (1995)
[5] Aravas, International Journal for Numerical Methods in Engineering 24 pp 1395– (1987) · Zbl 0613.73029
[6] Zhang, Computer Methods in Applied Mechanics and Engineering 121 pp 29– (1995)
[7] Mahnken, International Journal of Plasticity 15 pp 1111– (1999)
[8] Srikanth, International Journal for Numerical Methods in Engineering 45 pp 1569– (1999)
[9] Mühlich, Computational Mechanics 31 pp 479– (2003)
[10] Keavey, International Journal for Numerical Methods in Engineering 65 pp 679– (2006)
[11] . Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Inc.: Englewood Cliffs, NJ, 1983.
[12] Nonlinear Programming (2nd edn). Athena Scientific: Belmont, MA, 2003.
[13] Chaboche, International Journal of Plasticity 2 pp 149– (1986) · Zbl 0612.73038
[14] Chaboche, International Journal of Plasticity 2 pp 247– (1989) · Zbl 0695.73001
[15] Reed, International Journal of Plasticity 1 pp 63– (1985)
[16] Hughes, International Journal for Numerical Methods in Engineering 15 pp 1862– (1980)
[17] Nagtegaal, Computer Methods in Applied Mechanics and Engineering 33 pp 469– (1982)
[18] Weber, International Journal of Plasticity 6 pp 701– (1990)
[19] Healy, Computational Mechanics 9 pp 95– (1992)
[20] Ortiz, International Journal for Numerical Methods in Engineering 23 pp 353– (1986)
[21] Keavey, International Journal for Numerical Methods in Engineering 53 pp 1491– (2002) · Zbl 1112.74558
[22] ABAQUS Theory Manual. Version 6.6, Hibbit, Karlson & Sorensen, Inc., 2006.
[23] , , . Numerical Recipies in Fortran 77 (2nd edn). Cambridge University Press: Cambridge, 1992.
[24] Perez-Foguet, Computer Methods in Applied Mechanics and Engineering 189 pp 277– (2000)
[25] Simo, Computer Methods in Applied Mechanics and Engineering 48 pp 101– (1985)
[26] Miehe, Computer Methods in Applied Mechanics and Engineering 134 pp 223– (1996)
[27] Tvergaard, International Journal of Fracture 18 pp 237– (1982)
[28] . Computational Inelasticity. Springer: Berlin, second printing, 2000.
[29] Tvergaard, Journal of the Mechanics and Physics of Solids 35 pp 43– (1987)
[30] Tvergaard, Advances in Applied Mechanics 27 pp 83– (1990)
[31] Tvergaard, Journal of the Mechanics and Physics of Solids 34 pp 213– (1986)
[32] . Limits to ductility by plastic flow localization. In Mechanics of Sheet Metal Forming, (eds). Plenum: New York, 1978; 237–265. · doi:10.1007/978-1-4613-2880-3_10
[33] Needleman, Journal of the Mechanics and Physics of Solids 35 pp 151– (1987)
[34] Chu, Journal of Engineering Materials and Technology 102 pp 249– (1980)
[35] Tvergaard, Acta Metallurgica 32 pp 157– (1984)
[36] . Material strain-rate sensitivity in the round tensile bar. Brown University Report, Division of Engineering, 1985.
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.