Geodesic
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. 
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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/

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