Mihai Gologanu1, Jean‐Baptiste Leblond1, J. Devaux2
1Laboratoire de Mode´lisation en Me´canique, Universite´ Paris VI, Tour 66, 4 place Jussieu, 75252 Paris Cedex 05, France
2FRAMASOFT + CSI, 10 rue Juliette Re´camier, 69456 Lyon Cedex 06, France
Tóm tắt
The aim of this paper is to extend the classical Gurson (1977) analysis of a hollow rigid ideal-plastic sphere loaded axisymmetrically to an ellipsoidal volume containing a confocal oblate ellipsoidal cavity. An “expansion” velocity field satisfying conditions of homogeneous boundary strain rate is used to derive a two-field estimate of the overall yield criterion. The latter is shown to be reducible, with a few approximations, to a Gurson-like criterion depending on the “shape parameter” of the cavity. The accuracy of this estimate is assessed through comparison with some results derived from a numerical minimization procedure. An approximate evolution equation for the shape parameter is also presented; comparison with some finite element simulations suggests a slight modification of the theoretical formula leading to considerably enhanced agreement.
