3D printing enables the implementation of complex and customized components that would be difficult or impossible to realize using conventional production methods. The design and production of 3D-printed parts are heavily dependent on the resources available, as they have a significant influence on the final design and performance. Ideally, all conceivable material and geometry combinations could be tested to find the optimal combination. However, manually designing, printing and testing all these variants would be both time-consuming and costly. Software solutions such as the Carbon Design Engine enable the fast and intelligent selection, compilation and integration of geometries of desired mechanical properties in a lattice structure and allow the performance to be estimated without having to print physical parts beforehand.

How grid structures work

The design and printing of parts with lattice structures are a key benefit of additive manufacturing (AM) as they offer unique properties that cannot be replicated with conventional manufacturing methods. Some of the benefits of lattice components include energy absorption and recovery, comfort and even stress distribution, adaptability, increased breathability, and the ability for lighter construction.

The repeating pattern of each cell type has unique aesthetic and physical properties. The Voronoi pattern, for example, has a foam-like, non-linear stress-strain relationship that results in high energy release and an aesthetic honeycomb structure. In contrast, the Tetrahedron pattern has a flexural response suitable for comfort cushioning in a static environment and a triangular aesthetic.

Left: physical test; right: simulated test. © Carbon

Cell types can be combined to create zones with different properties within the same part. Hybrid cells combine two (or more) primary cells into a new cell, creating an infinite, continuously parameterized cell family. In a pattern, these hybrid cells can transition spatially into any other hybrid cell type via a self-consistent interpolation scheme that guarantees strut connectivity. The self-consistent interpolation scheme estimates values between data points as the cells transition spatially to ensure topological consistency inside the part. This means that the combinations and possibilities for creating a grid are endless. So how can designers find the right combination for a product? Designing, printing and testing even 100 of these possibilities would take months. Although this time is shorter than traditional manufacturing, Carbon can solve the problem using simulations and machine learning (ML).

Simulation of the load on a grid

To model such a complex system, Carbon needed a simulator that could accurately model large deformations, bending and contacts. Among these requirements, the handling of self-contact is the main bottleneck for simulators. Omitting these constraints and using a linear solver without contact would result in the calculated force-deformation response being unrealistically stiff, and the tool would not be able to accurately capture features such as plateau stress and compaction stiffness. Recently, NYU researchers proposed a state-of-the-art automated framework, called the Incremental Potential Contact (IPC) algorithm, which is capable of handling very complex multibody contact physics. IPC provides a contactless contact algorithm by introducing mechanistically based barrier energy functions.

With the help of IPC, Carbon carried out a high-resolution physical simulation on lattice cuboids. Using one of Carbon's elastomeric materials, they simulated the quasi-static loading of a lattice cell, taking into account contact and bending. They then performed a conventional physical validation test on a printed part with the same material and compared the simulated validation results with the physical validation results.

Using this process, Carbon was able to develop a neural operator that uses all this data to predict the mechanical response of a lattice puck. This is done using an attention mechanism that processes sequential data and long-range dependencies (like a transformer). Carbon can use automatic differentiation because all parameters are smooth, including those that determine the shape of the lattice. Using physical scaling rules, data could be generated for other elastomeric resins.

Metamaterials library

There are over 9,000 data sets in Carbon's metamaterials library, covering a wide range of mechanical reactions. Using the "Find Unit Cell" feature, a designer can define ranges for desired responses, lattice types and high-level geometric parameters, significantly narrowing the possibilities. Based on these options, designers can compare the nonlinear material response up to compaction for thousands of lattice structures. They can perform all these comparisons without having to simulate each option individually. With this data, lattice structures can be combined to create a single printable part with the exact properties required in each section. The Carbon Design Engine can perform these transitions effortlessly, ensuring printing with the required properties in each section, the company says.

Carbon continues to look for ways to improve the process. More lattice types will be added, including hexagonal-based unit cells and hybrid cells, as well as additional characterizations that will further optimize dynamic loading and make it available for more elastomeric materials as Carbon's material diversity continues to grow. The company is also working to develop better and more intuitive tools for designers.