Question:

What are the options for simulating lattices?

There are three main methods for simulating lattices in nTopology. They are using Solid Elements, Beam Elements, or Homogenization. The pros and cons of each method are listed in the table with an example workflow given below.

Type Pros Cons
• Accuracy
• Edge effects considered
• Locatable maximum stress point
• Computationally expensive
• Requires meshing of the lattice (challenging)
• Dependent on mesh quality
• Large file size
• Fastest
• Accepts field-driven beam thickness
• Only works on beam-based lattice structures
• No edge effects
• No stress concentrations
• Faster
• Works for any type of lattice
• Works on large and high-density lattice structures
• More setup steps
• Least accurate
• No edge effects
• No stress concentrations
• Lattice must be uniform

Solid Elements

Solid elements are a volumetric finite element mesh of the entire lattice structure.

• Small mesh size is required to capture the detail of the lattice

Set up an FE Solid Component block in the FE Model. Depending on the model, some mesh errors may occur. Follow these steps if so:

• Use Remesh Surface block after Mesh from Implicit Body
• Volume Mesh block may fail, if so, you can repair the mesh through Voxel Grid from Implicit and Remesh Surface or use the slower, more robust, Robust Tetrahedral Mesh

Beam Elements

Beam elements are finite element nodes along lattice vertices, connected by lattice beams. This method greatly reduces the number of elements from a typical volume mesh, but it ignores certain mechanical behavior like edge effects and stress concentrations in the lattice. FE nodes will be placed at the end points of each beam, along with node(s) along the subdivisions of the beam. You can choose the number of subdivisions as an input to the FE Lattice Mesh block, which will be arrayed as demonstrated in the image below.

Set up an FE Lattice Component in FE Model. Keep in mind the lattice beam thickness is a field input in the FE Lattice Component block. You will need to correctly isolate and trim the lattice elements.

• Use Trim Lattice to make sure the lattice elements lie within the volume of the Lattice Structure
• If you get a warning about short lattice beams, use Collapse Lattice Vertices with a threshold much lower than the unit cell size

Homogenization

To create a homogenized simulation, run a Solid FEA simulation on a single unit cell of the lattice, and generate effective material properties of the unit cell. Next, run a second Solid FEA simulation on the bulk lattice structure volume using the effective material properties (from the first simulation).

Use FE Solid Component with the Material chip from the Homogenization block.

• Works best with many unit cells
• Good for comparing different lattice types

Comparison

To compare these methods, we've created a BCC Lattice between two panels. Look for the download of this Case Study at the bottom of this article.

The images below represent a direct comparison in Displacement values and Von Mises Stress values. The images are in the same order as above (Solid Elements, Beam Elements, and Homogenization). Scroll below to see the range of values.

Below is the direct comparison of the three different methods, comparing computational time, stresses, and displacement.

Keywords:

analysis lattice shell design element solid component homogenize beam simulate homogenixation pro con methods