A stochastic constitutive model for disordered cellular materials: Finite-strain uni-axial compression

A stochastic constitutive model is developed for describing the continuum-scale mechanical response of disordered cellular materials. In the present work, attention is restricted to finite-strain uni-axial compression under quasi-static loading conditions. The development begins with an established cellular-scale mechanical model, but departs from traditional modeling approaches by generalizing the cellular-scale model to accommodate finite strain. The continuum-scale model is obtained by averaging the cellular-scale mechanical response over an ensemble of foam cells. Various stochastic material representations are considered through the use of probability density functions for the relevant material parameters, and the effects of the various representations on the continuum-scale response are investigated. Combining cellular-scale mechanics with a stochastic material representation to derive a continuum-scale constitutive model offers a promising new approach for simulating the finite-strain response of cellular materials. Results demonstrate that increasing a material’s degree of polydispersity can produce the same stiffening effects as increasing the initial solid-volume fraction. Additionally, particular stochastic material representations are shown to provide upper and lower bounds on the mechanical response of the cellular materials under investigation, while suitable choices for the stochastic representation are shown to accurately reproduce experimental stress–strain data through the large deformations associated with densification.