Constitutive modelling of open-porous neo-Hookean solids

Abstract

Open-porous materials exhibit pronounced compressibility, nonlinear densification, and power-law scaling of stiffness with density. In this work, we propose a thermodynamically consistent compressible neo-Hookean constitutive model for open-porous solids in which porosity serves as the primary governing variable. The strain-energy density is formulated to couple distortional elasticity of the solid skeleton with a volumetric response governed by deformation-induced porosity evolution, including a bounded representation of pore collapse. The formulation introduces a minimal set of parameters, namely the initial porosity, intrinsic skeleton moduli, and a scalar parameter controlling the onset of densification. A key feature of the model is a modified volumetric term in which the response is normalised by the current porosity, ensuring a physically consistent transition from a porous to a densified state without artificial stiffening. In the small-strain limit, the model recovers classical linear elasticity with effective moduli that may be chosen either from homogenisation bounds, such as the Hashin-Shtrikman estimates, or from Gibson-Ashby-type power-law scaling to capture topology-dependent behaviour. At finite strains, the formulation captures the characteristic nonlinear stiffening and convex stress-stretch response associated with progressive pore collapse. The proposed framework thus provides a compact, flexible, and extensible constitutive description that unifies effective-medium consistency with experimentally observed scaling behaviour, and is well suited for finite element implementation and multiscale modelling of highly compressible open-porous materials. The model is finally validated against available experimental data.