@Article{cmes.2001.002.063,
AUTHOR = {A. Le  van, P. Le  Grognec},
TITLE = {Modeling and Numerical Computation of Necking in Round Bars Using a Total Lagrangian Elastoplastic Formulation},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {2},
YEAR = {2001},
NUMBER = {1},
PAGES = {63--72},
URL = {http://www.techscience.com/CMES/v2n1/24719},
ISSN = {1526-1506},
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. <br/>
 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. <br/>
 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.},
DOI = {10.3970/cmes.2001.002.063}
}