# Lattice structures

**Why lattice ?**

Everybody knows that, with additive manufacturing (AM), we can produce metal structures starting from 3D digital models and we can obtain very complex geometries impossible to build with other methods.

Among these, the cellular (or lattice) structures are so called since they are made up of a unit modular cell that is periodically replicated to define the structure shape. Therefore, one of the main properties of these structures is that the relative density depends on the cell shape, not only on the parent material as usual. Then, structures made by the same material can have density gradients inside and, therefore, variable properties as stiffness and strength. The properties of the structure are scalable down to the properties of the constituent cells.

This concept is the same of metal foams, honeycomb panels and so on, however the lattice structures can be designed and built with unprecedented levels of detail and controlled variability.

**Cellular design**

The engineering of cellular materials is based on the correlation between the micro-scale of the single cell and the macro-scale of the entire structure. There are several methods to establish this correlation and some of them are very complicated in the theoretical formulation. The shape, dimensions, orientation and spatial distribution of the cell are parameters able to drive, and thus control, the structure properties: orthotropy, equivalent stress-strain, natural frequencies, failure modes, and cracks propagation directions.

**Calculations through the**** ****models**

The creation of simplified models to estimate the real behavior of cellular structures is challenging and time consuming. The geometrical complexity leads to complicated systems of equations that need too much time to be solved. Then, the main effort is given in developing compact models based on the homogenous equivalency at the macroscale.

The situation becomes more complex in case the elasto-plastic nonlinearity of the materials is included in the models, or when the dynamic response is needed. This is the case of impact energy absorption problems applied to lattice structures.

**Learning from experiments**

There is something surprising in observing the failure sequence of a functionally graded (that is, non-uniform cell distribution) lattice structure under compression. Here, the strength is literally shaped by the geometry created by the designer as most of the other properties.

Similarly, unexplored potentialities are evident in the fatigue lifetime evaluation of lattice structures. The deep comprehension on how to manage this complexity passes through the one-to-one validation of the theoretical models with experiments combined to the process-related parameters.

**Lattice as temporary supports for AM**

The metal AM needs temporary supports to sustain the part and to dissipate the thermal heating. They can be imposed by unclever algorithms... Or, better, we can design them as lattice structures with improved functions (auxetic behavior, thermal-controlled strain, etc.) For instance, we can shape the supports to be fully removed by sandblasting within a given time interval for all the surface orientations (steps 1-4 in the figure).

**Process control**

The process qualification and stabilization for the production of lattice structures is mandatory before starting any other activity, especially the experimental validation of samples. A lot of issues associated with the upskin and downskin profiles need to be fixed by selecting the right parameters linked to the volume energy density (VED) in laser powder bed fusion (L-PBF) processes. Then, the laser speed, the layer thickness, the laser power and other details are needed. How to know their exact combination? Our experience says that the machine's standard setup is not the good one. Instead, experimental campaigns associated with the design of experiments (DOE), the analysis of variance (ANOVA) and other statistical methods lead to the process optimization.