## 1 Introduction  
Additive manufacturing (AM) is a method whereby parts are manufactured by progressively depositing material layer by layer to achieve a desired shape. This differs from traditional (subtractive) manufacturing, where material is progressively removed from a parent block until it reaches the desired shape. Additive manufacturing can be performed in a variety of ways (including material-extrusion, powder-bed-fusion, binder-jetting, and stereolithography [1; 2]), each of which has unique benefits and drawbacks. Additive manufacturing in general, though, has a number of advantages over traditional (subtractive) manufacturing methods [3; 4; 5; 6; 7; 8]. One of these is the ability to manufacture lightweight parts which have an external skin and sparse internal infill. This decreases the weight of a part, which also decreases the amount of material required to manufacture the part. This, in turn, decreases the cost of the part in terms of machine-time, operator-time, and energy-consumption [9]. In order to design a part which takes advantage of this, however, it is first necessary to characterize the structural properties of the infill. There are a variety of infills commonly implemented in AM softwares, all of which have both benefits and drawbacks. The most common class of infills are the 2D infills (including the particularly common rectilinear infill) which are generated by printing the same pattern for every layer. This results in a structure that has a constant cross-section vertically (as if extruded in this direction). These infills have the advantage of simplicity, which makes them quick and reliable to print, but the infill geometry results in highly anisotropic structural properties. [PERSON] and [PERSON] [10; 11; 12], have developed methods of homogenizing the behavior of sparse rectilinear infills into orthotropic effective properties, which could be very useful for designing components using this infill. The next class of common infills is the 3D infills, such as cubic infill, which consist of a structure that spatially repeats in all three directions. Many of these exhibit cubic symmetry, which more closely approximates isotropic behavior. This benefit, however, comes at the cost of added complexity and more difficulty in printing. One infill that is particularly promising for future design work is the gyroid, a 3D infill based on a mathematical construct known as a triply periodic minimal surface. This infill is nearly isotropic, prints relatively quickly, and is quite strong [13; 14; 15]. All of these properties are very useful for simplifying design, but very little specific elastic property data is available in the literature. The final category of infills is the least well defined. It consists of those infills which do not fall into either of the previous categories due to their non-periodic nature, which often arises from optimization processes. These can take several forms, including using graded infills [16], internal structures containing voids [17; 18; 19], or internal structures with repeating optimized lattice structures which can be tuned to have specific elastic properties or graded to have spatially varying properties [19; 20; 21; 22; 23; 24; 25; 26; 27]. These repeating structures often take the form of standard rectangular, rhombic or hexagonal infill patterns whose properties have been studied in [28; 29; 30; 31]. Research has also been performed on strut-based lattices with spatially-varying strut-thicknesses [32; 33; 34; 35]. Several researchers have used topology optimization in order to directly tailor the microstructures to exhibit specific properties, thus allowing tuning of elastic moduli [24], Poisson's ratio [20], and general orthotropic properties [36]. [PERSON] et al. [36], developed a systematic analysis of stochastic foam-like infill materials, which can be tuned to nearly any set of orthotropic material properties. Most of these researchers have generated unique infill forms which are not readily implemented in existing slicing software.