Importance of the consideration of the specificities of local plastic deformation on the response of porous solids with Tresca matrix

Abstract

Abstract Based on rigorous limit-analysis theorems, very recently, Cazacu et al. (2014) have deduced an analytic plastic potential for porous solids with Tresca matrix. Key in the model development was the consideration of the specificities of the plastic flow of the matrix. In this paper, finite element calculations are conducted for a voided cubic cell obeying Tresca's criterion and compared with the predictions of the new model. The numerical calculations confirm the centro-symmetry of the yield locus of the porous Tresca material and the combined effects of the mean stress and the third-invariant of the stress deviator on void evolution. In particular, it is shown that the rate of void growth is faster for axisymmetric loading histories corresponding to the third-invariant J 3 Σ ≥ 0 than for those corresponding to J 3 Σ ≤ 0 , while void collapse occurs faster for loadings such that J 3 Σ ≤ 0 than for those characterized by J 3 Σ ≥ 0. Irrespective of the loading history, it is found that neglecting the local plastic heterogeneity leads to a drastic underestimation of the rate of void evolution.