Dynamic response of ductile materials containing cylindrical voids

The goal of this paper is to characterize the dynamic behavior of porous materials containing parallel cylindrical voids. Unlike static approaches, micro-inertia effects are accounted for in the modeling which infer a strong dependence of the dynamic response upon void geometry. Since cylindrical voids are considered, the void radius and void length both play a crucial role in the overall response of the porous material. A theoretical approach is developed, founded on the dynamic homogenization scheme proposed by Molinari and Mercier (J Mech Phys Solids 49:1497–1516, 2001) for spherical voids embedded in a viscoplastic matrix material. Considering a cylindrical unit cell, a constitutive response of porous material containing cylindrical void is developed for general homogeneous boundary conditions. For illustrative purpose, the analysis focuses on axisymmetric loadings considering a perfectly plastic matrix material. Micro-inertia effects are exemplified considering various loading conditions such as, among others, spherical loading and plane strain loading. In particular, the peculiar effect of the length of the cylindrical void is revealed. Indeed, particular attention has been paid to the response of short and elongated cylindrical voids. All predictions of the present model are verified against numerical simulations developed for various axisymmetric loading paths. Our findings can be used in several applications such as thick wall honeycomb structures or additively manufactured materials submitted to dynamic loading.