Lost in homogenisation: Navigating the challenges of predicting ideal behaviour in inhomogeneous porous structures

We introduce a novel meta-modelling approach coupled with a four-part piecewise constitutive model to predict the compressive behaviour of homogeneous foams using data from inhomogeneous specimens. This method estimates individual density layer responses within the foam, enabling the prediction of compression behaviour for ideal density configurations. Validated through cellulose pulp fibre foam experiments utilising Digital Image Correlation (DIC) analysis and finite element simulations of synthetic expanded polystyrene (EPS) foam, our meta-model effectively derives material properties from imperfect foams of varying densities, while accounting for errors induced by density variations. It accurately captures foam material response from initial compression through densification. Our approach offers significant advantages for optimising foam structures without costly commercial software or ideal specimens, bridging the gap between real-world materials and idealised models. While initially designed for cellulose pulp fibre foams, this model shows broad potential for evaluating various foams with density variations, including both sustainable and non-sustainable materials.