Derivation of a Lode angle dependent model for ductile porous materials: an extension of the stress-based variational approach

Long Cheng (1, 2) , Géry de Saxcé (2) , Djimédo Kondo (3)

1 LEM3 - Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux
2 LML - Laboratoire de Mécanique de Lille - FRE 3723
3 IJLRDA-MISES - Mécanique et Ingénierie des Solides Et des Structures

Recently, a new methodology of macroscopic modeling for ductile porous media has been proposed by the authors, using a statical limit analysis approach (Cheng et al., 2013). Since this model has been derived by considering a hollow sphere under axisymmetric loadings, only the effect of the sign of the stress deviator third invariant (or two values of Lode angle) has been investigated. The aim of the present paper is to extend the above mentioned stress-based model to the general case of non-axisymmetric loadings by introducing a more general trial stress field. The established new yield locus explicitly depends on the effect of the third invariant (equivalently the Lode angle). Finally, non negligible effects of the third stress deviator invariant on the voids growth rate is fully demonstrated. The results are fully illustrated.

Keywords: Ductile Porous material; von Mises matrix; Statical Limit Analysis; Third invariant of stress deviator

Domains: Structural mechanics [physics.class-ph]

Long Cheng, Géry de Saxcé, Djimédo Kondo. Derivation of a Lode angle dependent model for ductile porous materials: an extension of the stress-based variational approach. 2019. ⟨hal-02046987⟩