Strength Analysis of Anisotropic Porous Solids with Cylindrical Voids

This work analyzes the effective strength of porous solids with orthotropic matrix material, obeying Hill’s criterion and containing periodically distributed parallel cylindrical voids. The study considers both analytical and numerical evaluations. Analyzes are restricted to transversely isotropic materials under axisymmetric loading. In the theoretical side, a closed-form yield criterion is developed by means of a static analysis, which is expected to provide a lower bound to the overall strength. The analytical homogenized model consists of a simple parabolic function depending on the void volume fraction, the matrix material anisotropic strength properties, the mean lateral and Hill’s equivalent stresses. Theoretical results are compared with finite element calculations considering a cubic unit cell with a centered cylindrical void. Distinct material porosity and anisotropy levels as well as a wide range of stress triaxialities are considered. It is therefore possible to assess the combined effects of the material porosity and anisotropy on its effective macroscopic strength. Comparisons with the Benzerga-Besson upper bound are also carried out. Overall, the present model provides more conservative predictions in comparison with the Benzerga-Besson approach. Both analytical models coincide in the cases of longitudinal or purely hydrostatic loading. Comparison with the numerical results shows that the present model provides reasonably good predictions when compared to the finite element simulations, higher differences (up to \(20\%\)) being observed for lower porosities and higher stress triaxialities. The main outcome of this work is a closed-form yield function proving fairly accurate predictions to engineering applications, in which anisotropic porous solids with cylindrical voids are dealt with.