Numerical limit analysis and plasticity criterion of a porous Coulomb material with elliptic cylindrical voids

Franck Pastor; Joseph Pastor; Djimedo Kondo

doi:10.1016/j.crme.2014.12.004

Numerical limit analysis and plasticity criterion of a porous Coulomb material with elliptic cylindrical voids

Franck Pastor ¹; Joseph Pastor ²; Djimedo Kondo ³

¹ Athénée royal Victor-Horta, rue de la Rhétorique, 16, Bruxelles, Belgium
² Laboratoire LOCIE, UMR 5271 CNRS, Université de Savoie, 73376 Le Bourget-du-Lac, France
³ Institut Jean-Le-Rond-D'Alembert, UMR 7190 CNRS, UPMC, 75252 Paris cedex 05, France

Comptes Rendus. Mécanique, Volume 343 (2015) no. 3, pp. 199-209.

Abstract

The paper is devoted to a numerical Limit Analysis of a hollow cylindrical model with a Coulomb solid matrix (of confocal boundaries) considered in the case of a generalized plane strain. To this end, the static approach of Pastor et al. (2008) [18] for Drucker–Prager materials is first extended to Coulomb problems. A new mixed—but rigorously kinematic—code is elaborated for Coulomb problems in the present case of symmetry, resulting also in a conic programming approach. Owing to the good conditioning of the resulting optimization problems, both methods give very close bounds by allowing highly refined meshes, as verified by comparing to existing exact solutions. In a second part, using the identity of Tresca (as special case of Coulomb) and von Mises materials in plane strain, the codes are used to assess the corresponding results of Mariani and Corigliano (2001) [13] and of Madou and Leblond (2012) [11] for circular and elliptic cylindrical voids in a von Mises matrix. Finally, the Coulomb problem is investigated, also in terms of projections on the coordinate planes of the principal macroscopic stresses.

Received: 2014-10-12
Accepted: 2014-12-08
Published online: 2015-01-31

DOI: 10.1016/j.crme.2014.12.004

Keywords: Gurson-type models, Cylindrical voids, Porous Coulomb material, Micromechanics, Limit analysis, Static and mixed methods, Conic programming

Author's affiliations:

Franck Pastor ¹; Joseph Pastor ²; Djimedo Kondo ³

¹ Athénée royal Victor-Horta, rue de la Rhétorique, 16, Bruxelles, Belgium
² Laboratoire LOCIE, UMR 5271 CNRS, Université de Savoie, 73376 Le Bourget-du-Lac, France
³ Institut Jean-Le-Rond-D'Alembert, UMR 7190 CNRS, UPMC, 75252 Paris cedex 05, France

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     author = {Franck Pastor and Joseph Pastor and Djimedo Kondo},
     title = {Numerical limit analysis and plasticity criterion of a porous {Coulomb} material with elliptic cylindrical voids},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {199--209},
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     year = {2015},
     doi = {10.1016/j.crme.2014.12.004},
     language = {en},
}

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Franck Pastor; Joseph Pastor; Djimedo Kondo. Numerical limit analysis and plasticity criterion of a porous Coulomb material with elliptic cylindrical voids. Comptes Rendus. Mécanique, Volume 343 (2015) no. 3, pp. 199-209. doi : 10.1016/j.crme.2014.12.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.12.004/

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