EXACT RESULTS AND APPROXIMATE MODELS FOR POROUS VISCOPLASTIC SOLIDS

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 inter est, allows one to rederive in a simpler way some previous bounds of P onte-Castaneda and Talbot and Willis), and by exhibiting the exact for m of the overall potential of a typical porous viscoplastic volume ele ment, namely a hollow cylinder loaded in generalized plane strain. App roximate expressions for the macroscopic viscoplastic potentials of ma terials 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) reprodu ce the exact solution of a hollow cylinder or sphere loaded in hydrost atic tension or compression; (ii) be a quadratic form of the overall s tress tensor in the extreme case of a Newtonian (linear) behavior; and (iii) yield the currently accepted Gurson criterion in the other extr eme case of an ideal-plastic behavior.