### What types of lattices for additive manufacturing are there, and why are they so important? One of the advantages of AM is the ability to create fine-featured high precision shapes, and many designers have taken advantage of this and added lattice or cellular structures to their components. These structures can extend the capabilities of the part beyond what is possible using traditional manufacturing methods.

### In this series of posts about lattices, we’ll look at when to use lattice structures, how to successfully design them and the challenges associated with them. Let’s begin by explaining the terminology that AM engineers use when referring to lattice structures.

## What is a lattice structure using additive manufacturing techniques?

At Gen3D, we define lattice structures as meso-level design elements consisting of repeating unit cell elements in 3D space. With additive manufacturing, lattices bring many advantages. They reduce the mass of an object which means less material is used. Cellular structures can also give objects extra strength. You can see this concept in nature, such as cork, sea urchins, honeycomb and trabecular bone.

Lightweight and strong designs such as lattices reduce production costs, fuel use, and material waste. They have a host of other benefits as engineers move toward more optimised structures and begin to overcome the difficulties initially seen in their production. 2021 has already seen many success stories for lattice structures designed for additive manufacturing, especially in the medical field, including dental, prosthetics and bone regeneration.

## 3 common families of lattice structures

Lattice structures are incredibly important across all industries because they can be used to shape the physical properties of a part. There are three types of lattices for additive manufacturing. These are different subsets of lattice structures that should be used depending on the properties that you’re trying to achieve.

**The 3 most common families of lattice structures are:**

**Surface lattices**– lattices that are generated from trigonometric equations. Modifying the equation controls the shape, size and density of the 3D structure.**Strut lattices**– structures that consist of a series of rod-like forms that are connected in different orientations to form the different unit cells of the lattice.**Planar based lattices**– structures created as a periodic pattern in a 2D plane and then extruded in a single direction to create the 3D structure

## 1. Surface-based lattices

A subset of surface-based lattices are triply periodic minimal surfaces (TPMS). TPMS structures are defined using equations. A famous example is the gyroid lattice structure, which can be seen in the figure above. The gyroid structure is defined using the following equation:

**sin(x)cos(y) + sin(y)cos(z) + sin(z)cos(x)=0**

### TPMS structures

TPMS structures come in two different forms, these are known as sheet and skeletal-based surface lattices. Each of the TPMS lattices can be modified to have these forms and they can be created by toggling the double-skin checkbox in Gen3D’s software.

The sheet and skeletal versions of TPMS lattices can be used for different purposes, these can include bioscaffold for the skeletal based lattice and the high surface area to volume ratio of the sheet based TPMS structures makes them ideal for thermal management applications.

By modifying the equation different structures can be created. Over the years, researchers and mathematicians have derived many different structures based on this format. Many of these structures have been integrated into Gen3D’s lattice module.

## 2. Strut-based lattices

The next family of lattice structures are strut-based lattices. These are structures that consist of a series of rod-like forms that are connected in different orientations to form the different unit cells of the lattice. Some examples of these structures, that were created in Gen3D Lattice can be seen in the figure below.

As you can see, the way that the rods are connected can have a significant effect on the mechanical properties of the lattice structure. Traditionally, strut-based lattices have been the most common type of lattice structure, however, designing correctly with strut-based lattices can be challenging.

### Periodic and stochastic lattice structures

The way that the rods are connected also gives us another descriptor for strut-based lattices. Some lattices have the same repeating unit cell throughout the entire part. These are known as periodic lattices. The alternative to this is where the cells are connected randomly throughout the global structure. These are called stochastic lattice structures.

Stochastic lattices are commonly used in biomedical applications as they can be designed to closely match the properties of human bone and are therefore excellent for reconnecting with bone structures inside the body.

## 3. Planar lattices

The final category of meso-level design elements consisting of repeating unit cell elements in 3D space is the planar lattice. This can sometimes also be referred to as 2D or 2.5D lattices.

These structures are created as a periodic pattern in a 2D plane and then extruded in a single direction to create the 3D structure. An example can be seen in the following figure.

These structures are extremely useful when designing for minimal material usage (one of Gen3D’s four key principles of design for additive manufacturing) because they can be used wherever bulk material is present to reduce the mass and material required to print a part.

Planar lattices are the simplest type of lattice structure and can typically be created using any traditional CAD software as a BREP model. Our Sulis Lattice Module can also be used to create these types of structures for more complex shapes.

You can see how planar lattices can be used to remove material and create an aesthetically pleasing part in this design tutorial.

## Are all lattices uniform?

We’ve covered the basics terminology describing the different lattice families. However, these are still a couple more important terms that you need to know. Firstly, we need to describe whether the lattice is the same or changing through the part. To describe this, we introduce the terms homogeneous and heterogeneous lattices.

### Homogeneous lattice structures

A homogeneous lattice structure has uniform lattice properties across the entire part. However, with a heterogeneous lattice, one or more of the lattice properties are changing. Common properties that we may decide to change, include the density, wall thickness, or size of the unit cell.

### Heterogeneous lattice structures

Heterogeneous lattices are useful because we can tailor the properties of the lattice in specific regions of the part. For example, the density of the lattice can be driven from an FEA analysis. In areas, where the stress in the part is higher we can increase the density of the lattice and therefore increase the strength in that location.

## Conformal lattices

The final lattice descriptor that we will introduce in this post is a conformal lattice. Lattices can either be uniform in a design space or conform to the shape of the part. Conformal lattices can be set up to follow the contours of a part. This has the advantage of making the lattice look more appealing and more importantly, can also reduce stress concentrations building up as the boundaries of parts.

The following video shows how Gen3D software can be used to conform a lattice into a cylindrical coordinate frame.

It can be an interesting design exercise to modify coordinate frames because the results can often be counterintuitive. The following lattices were all created by using a diamond TPMS surface lattice but changing cylindrical coordinate space within a cubic part.

## Next steps in designing lattice structures

In this post, we’ve looked at how additive manufacturing design engineers describe the types of lattices that they design. In our next post about lattice structures, we’ll look at some applications for these types of structures in more detail.

If you’re interested in learning more about the design of lattice structures, then sign up for Gen3D’s Introduction to Design for Additive Manufacturing course.

Also, if you want to begin adding lattice structures to your components you can download a free 2-week trial of Gen3D’s Sulis Software at https://gen3d.com/download