Geodesic
Analysis of large elastic-plastic deformations: integration algorithm and numerical examples
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 4, pp. 509-517

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

An algorithm for investigation of elastic-plastic solids with regard to finite deformations has been developed. The kinematics of elastic-plastic deformations is based on multiplicative decomposition of the deformation gradient into elastic and inelastic parts. The stress state is determined by the Cauchy stress tensor. The constitutive equations have been obtained from the second law of thermodynamics with the introduction of the elastic free energy function. The elastic free energy function is formulated in an invariant form of the left Cauchy–Green tensor. The von Mises yield criterion with isotropic hardening has been used. The radial return method with an iterative refinement of the current state of deformation has been applied for dividing the elastic and plastic deformations. The principle of virtual work in terms of the virtual velocity has been used. The numerical implementation is based on the finite element method. The solution of the necking of a circular bar has been presented.
Keywords: nonlinear elasticity, finite deformations, plasticity. 
@article{UZKU_2017_159_4_a6,
     author = {L. U. Sultanov},
     title = {Analysis of large elastic-plastic deformations: integration algorithm and numerical examples},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {509--517},
     publisher = {mathdoc},
     volume = {159},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2017_159_4_a6/}
}
TY  - JOUR
AU  - L. U. Sultanov
TI  - Analysis of large elastic-plastic deformations: integration algorithm and numerical examples
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2017
SP  - 509
EP  - 517
VL  - 159
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZKU_2017_159_4_a6/
LA  - ru
ID  - UZKU_2017_159_4_a6
ER  - 
%0 Journal Article
%A L. U. Sultanov
%T Analysis of large elastic-plastic deformations: integration algorithm and numerical examples
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2017
%P 509-517
%V 159
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZKU_2017_159_4_a6/
%G ru
%F UZKU_2017_159_4_a6
L. U. Sultanov. Analysis of large elastic-plastic deformations: integration algorithm and numerical examples. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 4, pp. 509-517. http://geodesic.mathdoc.fr/item/UZKU_2017_159_4_a6/