Physically-based modeling of polymer foam microstructures: from realistic cellular microstructures and their variabilities to mechanical properties

Abstract

It is generally agreed that an efficient model for predicting the mechanical behavior of solid foams should present microstructural features similar to real ones. However, most theoretical results in foam micro-mechanics are based on periodic space-filling unit-cell which do not reflect the inherently random nature of real foams. The Kelvin cell or the Weaire-Phelan (WP) structure are by far the most used and yet they are only found in specialised foam. The present study therefore uses a versatile approach based on a thermodynamic description of interacting bubbles growth to produce representative volume elements of closed-cell foams with a wide variety of morphologies. Using a small set of parameters, one can build morphologies with local features specific to non-equilibrium foams. The behavior of the internal gas phase during the formation process is also modelled while assuming the absence of diffusion in the continuous medium. A sequence of mechanical micro-models is developed to study the complete compressive response ranging from the initial elastic response followed by the extensive plateau stress all the way up to the densification zone. An advanced structural analysis applied to solid foams is performed. The results are discussed in view of randomness of the cellular microstructure, anisotropic cell shape effects and inner gas pressure effect. Using regression-based approaches we attempted to build a framework capable of yielding cautious but meaningful conclusions about the relationship between topological parameters and mechanical properties. This is a major improvement over previous studies which lack variability in topological arrangement for 3D representative volume elements or which use periodic boundary conditions known to influence the way macroscopic instabilities develop.