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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 22 Jun 2024 04:03:39 GMT2024-06-22T04:03:39ZComparison of bifurcation analysis and maximum force criteria in the prediction of necking in stretched metal sheets
http://hdl.handle.net/10985/10271
Comparison of bifurcation analysis and maximum force criteria in the prediction of necking in stretched metal sheets
PEERLINGS, Ron; GEERS, Marc; ABED-MERAIM, Farid
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.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/102712015-01-01T00:00:00ZPEERLINGS, RonGEERS, MarcABED-MERAIM, Farid 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.Bifurcation analysis versus maximum force criteria in formability limit assessment of stretched metal sheets
http://hdl.handle.net/10985/10023
Bifurcation analysis versus maximum force criteria in formability limit assessment of stretched metal sheets
PEERLINGS, Ron; GEERS, Marc G.D.; ABED-MERAIM, Farid
The present contribution deals with the prediction of diffuse necking in the context of forming and stretching of metal sheets. For this purpose, two approaches are investigated, namely bifurcation and the maximum force principle, with a systematic comparison of their respective ability to predict necking. While the bifurcation approach is of quite general applicability, some restrictions are shown for the application of maximum force conditions. Although the predictions of the two approaches are identical for particular loading paths and constitutive models, they are generally different, which is even the case for elasticity, confirming the distinct nature of the two concepts. Closed-form expressions of the critical stress and strain states are derived for both criteria in elasto-plasticity and rigid-plasticity for a variety of hardening models. The resulting useful formulas in rigidplasticity are shown to also accurately represent the elasto-plastic critical states for small ratios of the hardening modulus with respect to Young's modulus. Finally, the well-known expression of Swift's diffuse necking criterion, whose foundations are attributed in the literature to the maximum force principle, is shown here to originate from the bifurcation approach instead, providing a sound justification for it.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/100232014-01-01T00:00:00ZPEERLINGS, RonGEERS, Marc G.D.ABED-MERAIM, Farid The present contribution deals with the prediction of diffuse necking in the context of forming and stretching of metal sheets. For this purpose, two approaches are investigated, namely bifurcation and the maximum force principle, with a systematic comparison of their respective ability to predict necking. While the bifurcation approach is of quite general applicability, some restrictions are shown for the application of maximum force conditions. Although the predictions of the two approaches are identical for particular loading paths and constitutive models, they are generally different, which is even the case for elasticity, confirming the distinct nature of the two concepts. Closed-form expressions of the critical stress and strain states are derived for both criteria in elasto-plasticity and rigid-plasticity for a variety of hardening models. The resulting useful formulas in rigidplasticity are shown to also accurately represent the elasto-plastic critical states for small ratios of the hardening modulus with respect to Young's modulus. Finally, the well-known expression of Swift's diffuse necking criterion, whose foundations are attributed in the literature to the maximum force principle, is shown here to originate from the bifurcation approach instead, providing a sound justification for it.Analyse de bifurcation et critères de force maximum dans la prédiction des limites de striction des tôles métalliques étirées
http://hdl.handle.net/10985/10113
Analyse de bifurcation et critères de force maximum dans la prédiction des limites de striction des tôles métalliques étirées
PEERLINGS, Ron; GEERS, Marc; ABED-MERAIM, Farid
Cette contribution porte sur la prédiction de la striction diffuse dans le contexte des tôles métalliques sous changements biaxiaux. A cette fin, deux approches sont considérées, à savoir la théorie de bifurcation et le principe de force maximum, avec une analyse critique et une comparaison systématique de leurs prédictions respectives. L’expression bien connue du critère de striction diffuse de Swift, dont l’origine est attribuée au principe de force maximum, est montrée ici découler de l’approche de bifurcation, ce qui permet de lui donner une justification et des fondements plus solides.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/101132015-01-01T00:00:00ZPEERLINGS, RonGEERS, MarcABED-MERAIM, Farid Cette contribution porte sur la prédiction de la striction diffuse dans le contexte des tôles métalliques sous changements biaxiaux. A cette fin, deux approches sont considérées, à savoir la théorie de bifurcation et le principe de force maximum, avec une analyse critique et une comparaison systématique de leurs prédictions respectives. L’expression bien connue du critère de striction diffuse de Swift, dont l’origine est attribuée au principe de force maximum, est montrée ici découler de l’approche de bifurcation, ce qui permet de lui donner une justification et des fondements plus solides.