Numerical investigation of a~model problem for deforming an elastoplastic body with a~crack under non-penetration condition
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 4, pp. 335-344
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The Lamé system is considered in a two-dimensional domain with a crack. The Dirichlet and the Neuman conditions are held on the exterior boundary, and non-penetration condition is assumed to be on a crack. The convolution product of the deviator of the stress tensor is restricted by a certain constant within the domain. Thus, we have a model problem for deforming an ideal elastoplastic body with a crack (the Henky model) subject to the Mises yield criterion. Simultaneously, the non-penetration condition is held on a crack. The problem is formulated as a variational one. We find a displacement vector as solution to minimization problem for the energy functional over a convex set. Discretization of the problem is provided by a finite element method. Examples of calculation are obtained using the Udzava algorithm.
@article{SJVM_2006_9_4_a1,
author = {E. V. Vtorushin},
title = {Numerical investigation of a~model problem for deforming an elastoplastic body with a~crack under non-penetration condition},
journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
pages = {335--344},
publisher = {mathdoc},
volume = {9},
number = {4},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SJVM_2006_9_4_a1/}
}
TY - JOUR AU - E. V. Vtorushin TI - Numerical investigation of a~model problem for deforming an elastoplastic body with a~crack under non-penetration condition JO - Sibirskij žurnal vyčislitelʹnoj matematiki PY - 2006 SP - 335 EP - 344 VL - 9 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SJVM_2006_9_4_a1/ LA - ru ID - SJVM_2006_9_4_a1 ER -
%0 Journal Article %A E. V. Vtorushin %T Numerical investigation of a~model problem for deforming an elastoplastic body with a~crack under non-penetration condition %J Sibirskij žurnal vyčislitelʹnoj matematiki %D 2006 %P 335-344 %V 9 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/SJVM_2006_9_4_a1/ %G ru %F SJVM_2006_9_4_a1
E. V. Vtorushin. Numerical investigation of a~model problem for deforming an elastoplastic body with a~crack under non-penetration condition. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 4, pp. 335-344. http://geodesic.mathdoc.fr/item/SJVM_2006_9_4_a1/