Mechanics and modeling of hierarchically porous metamaterials manufactured by foaming fused deposition modeling

Hierarchically porous materials show promise across many applications due to their high specific strength, energy absorption, and damage tolerance. They are limited, however, by manufacturing and scaleability challenges, often requiring additive manufacturing techniques with nanoscale resolution, making them complex, slow, and/or expensive. Recent advances in commercially available foaming filaments for fused deposition modeling offer new possibilities for improved scaleability in manufacturing hierarchically porous metamaterials. In this study, the processing, microstructure, and resulting properties of foamed polylactic acid are characterized in detail. Foam collapse is observed at high extrusion temperatures, resulting in degradation of mechanical properties. Using a calibrated set of processing parameters, hierarchically porous materials can be produced with controllable porosity and accurate dimensions, by combining printed foam with designed gyroid structures. By varying the proportion of porosity located at the microscale (η) the mechanical behavior can be influenced. Shifting 5%–15% of the porosity from the macroscale to the microscale changes deformation mode from stretch- to bend-dominated, avoiding sudden post-yield softening. For absorbing low levels of energy, hierarchically porous materials with high η are superior due to the lower peak stress reached, while for higher levels of energy, they reach densification, resulting in comparable or greater peak stress than those materials with low η. Hierarchical application of the Gibson–Ashby model based on monoscale porous material data provides a reasonable approximation to the measured properties of hierarchical materials, though future improved modeling of monoscale porous materials should provide more accurate prediction.