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ARTICLE

Modeling and Numerical Computation of Necking in Round Bars Using a Total Lagrangian Elastoplastic Formulation

A. Le van¹, P. Le Grognec¹

1 Laboratoire de Mécanique et Matériaux, Division Mécanique des Structures, Ecole Centrale de Nantes. 1, rue de la Noë, BP 92101 - 44321 Nantes cedex 3, France

Computer Modeling in Engineering & Sciences 2001, 2(1), 63-72. https://doi.org/10.3970/cmes.2001.002.063

Abstract

Necking is a bifurcation phenomenon observed in round bars under tensile loading and has been investigated in numbers of papers. In the present work, it is modeled within the framework of finite rate-independent plasticity. The theory is based on thermodynamic foundations developed for standard materials and results in a total Lagrangian formulation for finite plasticity, where the total strain is decomposed additively according to [Green and Nagdhi 1965)] and the hardening is characterized by a nonlinear isotropic hardening law of the saturation type.
The discretization and consistent linearization of the elastic-plastic equation set using the standard finite element procedure lead to a low-cost algorithm, robust enough to deal with necking problems.
The numerical computations of necking are performed on cylindrical bars with various boundary condition types and the corresponding results compared with those obtained in the literature.

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