Towards a virtual functionally graded foam: Defining the large strain constitutive response of an isotropic closed cell polymeric cellular solid

Functionally graded materials have been defined by Hirai [1] to be “a new generation of engineered materials wherein the microstructural details are spatially varied through a non-uniform distribution of the reinforcement phase(s)…”. Extending this paradigm to the field of cellular solids, a functionally graded foam material (FGFM) may be thought of as a foam for which microstructural features such as cell size, and strut and wall (for closed cell foams) thickness vary in a continuous manner across the volume of the foam. These features may be varied globally by variation of the foam’s density, ρf. Cui et al. [2] and Kiernan et al. [3] have shown some potential benefits of FGFMs under dynamic conditions using discretely layered finite element foam models. In their work the ABAQUS crushable foam model defines the constitutive response of each element layer of a regularly shaped specimen. The density, and corresponding Young’s modulus, Ef, and hardening law of each layer is unique, thus defining a quasi-graded response. Motivated by their results, this paper attempts to describe the large strain compressive response of a gas filled EPS foam such that it may, in a future work, be incorporated into the framework of a user written finite element in which constitutive properties may be graded according to simple polynomials. Experimental data is gathered from a number of expanded polystyrene foam specimens of different densities, and important foam characteristics are defined as functions of ρf. Results compare excellently to those of the ABAQUS foam model, and limitations of the modelling approach are discussed.