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R. Hill, “On Discontinuous Plastic States, with Special Reference to Localized Necking in Thin Sheets,” Journal of the Mechanics and Physics of Solids, Vol. 1, No. 1, 1952, pp. 19-30. doi:10.1016/0022-5096(52)90003-3

has been cited by the following article:

• TITLE: Theoretical and Numerical Comparison of Limit Point Bifurcation and Maximum Force Criteria. Application to the Prediction of Diffuse Necking

  AUTHORS: Guillaume Altmeyer

  KEYWORDS: Forming; Bifurcation Analysis; Maximum Force Criterion; Diffuse Necking; Forming Limit Diagram

  JOURNAL NAME: Modeling and Numerical Simulation of Material Science, Vol.3 No.1, January 21, 2013

  ABSTRACT: A large number of criteria has been developed to predict material instabilities, but their choice is limited by the lack of existing comparison of their theoretical basis and application domains. To overcome this limitation, a theoretical and numerical comparison of two major models used to predict diffuse necking is present in this paper. Limit Point Bifurcation criterion is first introduced. An original formulation of the Maximum Force Criterion (MFC), taking into account the effects of damage and isotropic and kinematic hardenings, is then proposed. Strong connections are shown between them by comparing their theoretical basis. Numerical Forming Limit Diagrams at diffuse necking obtained with these criteria for different metallic materials are given. They illustrate the theoretical link and similar predictions are shown for both models.