In this work we consider a solid body $\Omega \subset {\mathbb{R}}^{3}$ constituted by a nonhomogeneous elastoplastic material, submitted to a density of body forces $\lambda f$ and a density of forces $\lambda g$ acting on the boundary where the real $\lambda $ is the loading parameter. The problem is to determine, in the case of an unbounded convex of elasticity, the Limit load denoted by $\overline{\lambda}$ beyond which there is a break of the structure. The case of a bounded convex of elasticity is done in [El-Fekih and Hadhri, RAIRO: Modél. Math. Anal. Numér. 29 (1995) 391-419]. Then assuming that the convex of elasticity at the point x of $\Omega $, denoted by K(x), is written in the form of ${\text{K}}^{D}\left(x\right)+\mathbb{R}\text{I}$, I is the identity of ${{\mathbb{R}}^{9}}_{sym}$, and the deviatoric component ${\text{K}}^{D}$ is bounded regardless of x $\in \Omega $, we show under the condition “Rot f $\ne 0$ or g is not colinear to the normal on a part of the boundary of $\Omega $”, that the Limit Load $\overline{\lambda}$ searched is equal to the inverse of the infimum of the gauge of the Elastic convex translated by stress field equilibrating the unitary load corresponding to $\lambda =1$; moreover we show that this infimum is reached in a suitable function space.

@article{M2AN_2005__39_4_637_0, author = {Elyacoubi, Adnene and Hadhri, Taieb}, title = {Characterization of the limit load in the case of an unbounded elastic convex}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {637--648}, publisher = {EDP-Sciences}, volume = {39}, number = {4}, year = {2005}, doi = {10.1051/m2an:2005028}, mrnumber = {2165673}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2005028/} }

TY - JOUR AU - Elyacoubi, Adnene AU - Hadhri, Taieb TI - Characterization of the limit load in the case of an unbounded elastic convex JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2005 SP - 637 EP - 648 VL - 39 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005028/ DO - 10.1051/m2an:2005028 LA - en ID - M2AN_2005__39_4_637_0 ER -

%0 Journal Article %A Elyacoubi, Adnene %A Hadhri, Taieb %T Characterization of the limit load in the case of an unbounded elastic convex %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2005 %P 637-648 %V 39 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005028/ %R 10.1051/m2an:2005028 %G en %F M2AN_2005__39_4_637_0

Elyacoubi, Adnene; Hadhri, Taieb. Characterization of the limit load in the case of an unbounded elastic convex. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 (2005) no. 4, pp. 637-648. doi : 10.1051/m2an:2005028. http://www.numdam.org/articles/10.1051/m2an:2005028/

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