Comparison of bifurcation analysis and maximum force criteria in the prediction of necking in stretched metal sheets

F. Abed-Meraim; R.H.J. Peerlings; M.G.D. Geers

Comparison of bifurcation analysis and maximum force criteria in the prediction of necking in stretched metal sheets

F. Abed-Meraim, R.H.J. Peerlings, M.G.D. Geers

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

In the present work, diffuse necking is investigated for stretched metal sheets using two different approaches, namely bifurcation theory and maximum force principle. The contribution includes a critical analysis and a systematic comparison of their respective ability to predict necking. In particular it is shown that, in contrast to bifurcation theory, which is of quite general applicability, some restrictions are associated with the application of maximum force conditions. It is noteworthy that the well-known Swift diffuse necking criterion is recovered through bifurcation analysis. Recall that Swift's criterion has long been attributed in the literature to the maximum force principle, while it is shown here to rather originate from the bifurcation analysis, which provides it with a sound theoretical justification.

Original language	English
Title of host publication	Proceedings of the 8th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2015
Editors	E. Oñate, D.R.J. Owen, D. Peric, M. Chiumenti
Publisher	International Center for Numerical Methods in Engineering (CIMNE)
Pages	182-193
Number of pages	12
ISBN (Print)	9788494424465
Publication status	Published - 2015
Event	13th International Conference on Computational Plasticity. Fundamentals and Applications (COMPLAS 2015), September 1-3, 2015, Barcelona, Spain - Barcelona, Spain Duration: 1 Sept 2015 → 3 Sept 2015 http://congress.cimne.com/complas2015/frontal/default.asp

Conference

Conference	13th International Conference on Computational Plasticity. Fundamentals and Applications (COMPLAS 2015), September 1-3, 2015, Barcelona, Spain
Abbreviated title	COMPLAS 2015
Country/Territory	Spain
City	Barcelona
Period	1/09/15 → 3/09/15
Other	"Fundamentals and Applications"
Internet address	http://congress.cimne.com/complas2015/frontal/default.asp

Keywords

Bifurcation analysis
Critical necking strains
Diffuse necking
Formability limits
Maximum force criteria
Stretched metal sheets

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Abed-Meraim, F., Peerlings, R. H. J., & Geers, M. G. D. (2015). Comparison of bifurcation analysis and maximum force criteria in the prediction of necking in stretched metal sheets. In E. Oñate, D. R. J. Owen, D. Peric, & M. Chiumenti (Eds.), Proceedings of the 8th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2015 (pp. 182-193). International Center for Numerical Methods in Engineering (CIMNE).

Abed-Meraim, F. ; Peerlings, R.H.J. ; Geers, M.G.D. / Comparison of bifurcation analysis and maximum force criteria in the prediction of necking in stretched metal sheets. Proceedings of the 8th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2015. editor / E. Oñate ; D.R.J. Owen ; D. Peric ; M. Chiumenti. International Center for Numerical Methods in Engineering (CIMNE), 2015. pp. 182-193

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Abed-Meraim, F, Peerlings, RHJ & Geers, MGD 2015, Comparison of bifurcation analysis and maximum force criteria in the prediction of necking in stretched metal sheets. in E Oñate, DRJ Owen, D Peric & M Chiumenti (eds), Proceedings of the 8th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2015. International Center for Numerical Methods in Engineering (CIMNE), pp. 182-193, 13th International Conference on Computational Plasticity. Fundamentals and Applications (COMPLAS 2015), September 1-3, 2015, Barcelona, Spain, Barcelona, Spain, 1/09/15.

Comparison of bifurcation analysis and maximum force criteria in the prediction of necking in stretched metal sheets. / Abed-Meraim, F.; Peerlings, R.H.J.; Geers, M.G.D.
Proceedings of the 8th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2015. ed. / E. Oñate; D.R.J. Owen; D. Peric; M. Chiumenti. International Center for Numerical Methods in Engineering (CIMNE), 2015. p. 182-193.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AB - In the present work, diffuse necking is investigated for stretched metal sheets using two different approaches, namely bifurcation theory and maximum force principle. The contribution includes a critical analysis and a systematic comparison of their respective ability to predict necking. In particular it is shown that, in contrast to bifurcation theory, which is of quite general applicability, some restrictions are associated with the application of maximum force conditions. It is noteworthy that the well-known Swift diffuse necking criterion is recovered through bifurcation analysis. Recall that Swift's criterion has long been attributed in the literature to the maximum force principle, while it is shown here to rather originate from the bifurcation analysis, which provides it with a sound theoretical justification.

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Abed-Meraim F, Peerlings RHJ , Geers MGD. Comparison of bifurcation analysis and maximum force criteria in the prediction of necking in stretched metal sheets. In Oñate E, Owen DRJ, Peric D, Chiumenti M, editors, Proceedings of the 8th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2015. International Center for Numerical Methods in Engineering (CIMNE). 2015. p. 182-193

Comparison of bifurcation analysis and maximum force criteria in the prediction of necking in stretched metal sheets

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