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Communication Dans Un Congrès Année : 2000

Modeling and computation of necking instability in round bars using a total lagrangian elastoplastic formulation

Résumé

Necking is an instability phenomenon observed in round bars under tensile loading and has been investigated in numbers of works. In the present work, it is modeled within the framework of finite rate-independent plasticity. The theory is based on thermodynamical foundations for standard materials 1 and results in a total Lagrangian formulation for finite plasticity. The total strain is decomposed additively according to Green and Nagdhi 2. The yield function is of von Mises type and depends on the symmetric Piola-Kirchhoff stress tensor. Considering nonlinear isotropic hardening, the hardening law is written in the form of an exponential function. However, here it relates Lagrangian (material) variables, namely the Lagrangian hardening variable and the Lagrangian effective plastic strain. The local integration is carried out using the fully implicit integration scheme (backward Euler difference scheme), which ensures both the stability and the symmetry of the consistent tangent modulus. The numerical implementation is simple as it works with classical finite elements. For the necking problem considered herein the proposed algorithm is robust enough to pass through the first critical point with no use of line-search. The numerical computations are performed both on shear free end bars including an initial small geometrical defect and geometrically perfect bars with gripped ends. The derived load-displacement curve compares very well with those obtained in the literature, although the material considered and particularly the formulations adopted are quite different.
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Dates et versions

hal-01381102 , version 1 (14-10-2016)

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  • HAL Id : hal-01381102 , version 1

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Anh Le Van, Philippe Le Grognec. Modeling and computation of necking instability in round bars using a total lagrangian elastoplastic formulation. European Congress on Computational Methods in Applied Sciences and Engineering, Sep 2000, Barcelone, Spain. ⟨hal-01381102⟩
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