Numerical limit analysis bounds for ductile porous media with oblate voids

Franck Pastor (1) , Djimedo Kondo (1) , Joseph Pastor (2)

1 LML - Laboratoire de Mécanique de Lille - FRE 3723
2 LOCIE - LabOratoire proCédés énergIe bâtimEnt

The paper is devoted to a numerical limit analysis of a hollow spheroidal model with a von Mises solid matrix. To this purpose, existing kinematic and static 3D-FEM codes for the case of spherical cavities have been modified and improved to account for the model of a spheroidal cavity confocal with the external spheroidal boundary. The optimized conic programming formulations and the resulting codes appear to be very efficient. This framework is then applied to the derivation of numerical upper and lower anisotropic bounds in the case of an oblate void. The numerical results obtained from a series of tests are presented and allow to assess the accuracy of closed-form expressions of the macroscopic criteria proposed by (Gologanu et al., 1994) and (Gologanu et al., 1997) for porous media with oblate voids.

Mots clés: Gurson-type models; Spheroidal voids; Micromechanics; Limit analysis; Upper and lower bounds; Conic programming

Franck Pastor, Djimedo Kondo, Joseph Pastor. Numerical limit analysis bounds for ductile porous media with oblate voids. Mechanics Research Communications, 2011, 38 (5), pp.350-354. ⟨10.1016/j.mechrescom.2011.02.001⟩. ⟨hal-00607929⟩