A sigmoidal equation for the high strain rate compression of porous metals

The high strain rate compression of porous materials is a problem that presents a series of difficulties to continuum-scale codes, its computational cost being a major one. Following previous contributions suggesting that compaction can be defined in terms of volumetric strain, we propose to model the compaction of porous metals by means of a sigmoidal equation. The definition requires only four parameters, each of them with a physical meaning. We tested the proposed equation against molecular dynamics simulations of high strain rate compression of closed-cell and open-cell foams, as well as micro-scale data available in the literature. The equation can be used in micro and macro-scale codes where nano-scale porosity cannot be modeled explicitly.