Macroscopic yield criteria for ductile materials containing spheroidal voids: An Eshelby-like velocity fields approach

• We determine the yield surface of ductile materials containing spheroidal voids.
• We consider trial velocity fields inspired from the Eshelby inclusion problem.
• The criterion show significant effects of transverse and longitudinal shear stresses.

Making use of limit analysis theory, we derive a new expression of the macroscopic yield function for a rigid ideal-plastic von Mises matrix containing spheroidal cavities (oblate or prolate). Key in the development of the new criterion is the consideration of Eshelby-like velocity fields which are built by taking advantage of the solution of the equivalent inclusion problem in which the eigenstrains rate are unknown for the plasticity problem. These heterogeneous trial velocity fields contain non-axisymmetric components which prove to be original in the context of limit analysis of hollow spheroid. After carefully computing the macroscopic plastic dissipation and implementing a minimization procedure required by the use of the Eshelby-like velocity fields, we derive, for the porous medium, a two-field estimate of the anisotropic yield criterion whose closed-form expression is provided. This estimate is compared to existing criteria based on limit analysis theory. Interestingly, in contrast to these criteria, the new results predict a significant effect of shear loadings in the particular case of ductile materials weakened by penny-shaped cracks.