Homogenization of additive manufactured polymeric foams with spherical cells

Exciting progress in additive manufacturing (AM) technology, which enables fabrication of cellular structures with highly complex lattices and pores, has stimulated the development of lightweight structural products with improved performance and increased functionality. However, conventional design and analysis tools lack the ability to optimize complex geometries efficiently and robustly. With this motivation, in this study, homogenized material models of open-cell polymeric foams with spherical cell architectures that are manufactured by using an AM technology are formulated through both experimental and numerical investigations, which in turn can be employed in a novel micromechanics based topology optimization algorithm developed for the optimization of cellular structures. In this regard, generating computer aided drawing (CAD) data, which is mandatory for AM, randomly intersected spherical ensemble method is employed. Several foam models with different porosities are generated, and utilized in nonlinear finite element analyses (FEAs) to determine constitutive elastic constants. Plastic stress-strain data for the bulk AM material are obtained through static tensile tests in a variety of different loading directions and these results used in FEA as true stress-strain data. Homogenization is performed based on a quadratic form of the widely used Gibson and Ashby foam model, which describes the Young's modulus E∗ and yield strength σpl∗ of cellular structures in terms of relative density. Coefficients of the quadratic scaling laws are fitted by both FEA and experiments which are compared with each other.