Analysis of the mechanical behavior of porous materials containing two populations of voids under dynamic spherical loading

A computational homogenization analysis is performed on three-dimensional representative volume elements (RVE) that contain two distinct populations of voids, to demonstrate the influence of the interaction between cavities. RVEs are constructed as cubic elastic perfectly-plastic matrices embedding two families of spherical voids, and subjected to dynamic loading under homogeneous kinematic boundary conditions. Multiple microstructure models are considered by varying the number, position, and size of voids to evaluate the micro-inertia contribution to the overall macroscopic stress. Velocity fields within numerical RVEs are investigated to reveal the interaction of voids and their key role in the dynamic macroscopic response of the porous material. Based on numerical simulation results, a homogenization analytical model considering void interaction is proposed to describe the mechanical behavior under dynamic loadings. This model relies on adjusting the strain rate level at the boundary of unit cells composing the porous material. Comparison between our numerical and analytical results with those obtained using the classical Taylor homogenization scheme highlights the limitations of the Taylor model in the case of porous materials under dynamic loading.