TY  - EJOU
AU  - van, A. Le  
AU  - Grognec, P. Le  

TI  - Modeling and Numerical Computation of Necking in Round Bars Using a Total Lagrangian Elastoplastic Formulation
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2001
VL  - 2
IS  - 1
SN  - 1526-1506

AB  - 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.
KW  - elastoplasticity
KW  -  necking bifurcation
KW  -  total Lagrangian formulation
KW  -  finite element analysis

DO  - 10.3970/cmes.2001.002.063