Theoretical and numerical analysis of void coalescence in porous ductile solids under arbitrary loadings

Micromechanics-based constitutive relations are developed to model plasticity in solids with relatively high levels of porosity. They are especially appropriate to model void coalescence in ductile materials. The model is obtained by limit analysis of a cylindrical cell containing a coaxial void of finite height with plastic flow confined to the ligaments, and loaded under combined tension and shear. Previously obtained analytical estimates were not upper-bound preserving when shear was present and, in addition, were assessed against numerical results obtained for different cell geometries. Here, a rigorous upper-bound model is developed and its predictions are consistently compared with finite-element based estimates of limit loads on the same cylindrical unit cell exploiting quasi-periodic boundary conditions. The numerical results are used to guide a heuristic modification of the model in order to capture the behavior for extremely flat or extremely elongated voids.