Gurson's Criterion Research Articles

Effective properties of porous ideally plastic or viscoplastic materials containing rigid particles

This study deals with the overall yield surface of porous materials containing rigid inclusions and governed by a generalized Gurson model. The dissipation potential of these voided materials can be obtained in a closed form. An estimate for the effective dissipation potential of the composite is derived in terms of the strain energy of a linear comparison solid. The corresponding yield surface is described by a generalized Gurson criterion. These results are extended to voided viscous matrices. The accuracy of the analytical estimates is assessed by comparison with cell calculations performed by the finite element method.

Exact results and approximate models for porous viscoplastic solids

Abstract The aim of this paper is to present new approximate macroscopic models for porous viscoplastic materials, based on partial but exact results applicable to such media. Available results are first supplemented by providing a new inequality (which, in addition to its intrinsic interest, allows one to rederive in a simpler way some previous bounds of Ponte-Castaneda and Talbot and Willis), and by exhibiting the exact form of the overall potential of a typical porous viscoplastic volume element, namely a hollow cylinder loaded in generalized plane strain. Approximate expressions for the macroscopic viscoplastic potentials of materials containing cavities of cylindrical or spherical shape are then proposed, based on these and other results; these expressions satisfy, in particular, the three following natural requirements: (i) reproduce the exact solution of a hollow cylinder or sphere loaded in hydrostatic tension or compression; (ii) be a quadratic form of the overall stress tensor in the extreme case of a Newtonian (linear) behaviour; and (iii) yield the currently accepted Gurson criterion in the other extreme case of an ideal-plastic behavior.

Yield Criteria for Ductile Porous Solids

The present article reexamines the form of Gurson's criterion for isotropic porous solids, under hydrostatic and deviatoric stress loading. Two types of periodic spherical void spacings were considered, namely, cubical and hexagonal.