Printing path-dependent two-scale models for 3D printed planar auxetics by material extrusion

One particularly interesting class of mechanical metamaterials are those having a negative Poisson's ratio, which are referred to as 'auxetics'. Because of their geometrical complexity, auxetic designs cannot always be easily created. However, Additive Manufacturing (AM) methods like material extrusion in 3D printing present the opportunity to construct auxetic structures. Nevertheless, extruded 3D printed material can be highly anisotropic. Before 3D printed auxetics manufactured through material extrusion can be used in engineering applications, it is important to generate powerful simulation tools that can reliably reproduce and foretell their mechanical characteristics irrespective of their form and intricacy. In view of this, the current work proposes printing path-dependent models based on an experimentally validated multi-scale modelling scheme using the Lattice Beam Model (LBM). This is done by first representing idealized microstructures of extruded 3D printed polymers through geometric models and simulating these on the material scale. The aim is to explicitly model the inter-layer and intra-layer bonds that exist in material extruded 3D printed parts by assigning experimentally obtained interface properties that significantly differ from the bulk material. On the auxetic structure scale, two planar auxetic designs are modelled using the determined material scale relationships as input: Re-Entrant (RE) and Rotating Square (RS). In terms of mechanical response, the experimentally and numerically obtained force displacement curves agree reasonably well: the stiffness of the modelled auxetic designs fit well with the experimentally measured ones while the LBM simulations generally provide a good estimation in strength. Finally, it has been shown on both the material and auxetic structure scales that incorporation of the interfacial bond strengths in simulations of extruded 3D printed polymers is important, because neglecting these results in significant overestimation of the strength.