Lattice Search

25min
Find unit cells to meet the performance and aesthetic criteria for your designs in Design Engine's metamaterials library.
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﻿Filters﻿﻿
﻿Lattice Search Demo﻿﻿
﻿Foam to Lattice Workflow﻿﻿
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Launch Lattice Search from the quick-access button on the upper right of the design user interface.
 
You can also launch Lattice Search from inside the Strut Lattice tool, under Lattice Type﻿. This will enable you to apply unit cell from your search directly to an input mesh, as shown in the demo video below.
Filters
Thousands of lattices are available in the metamaterials library and Design Engine provides filter options to narrow your results by performance and by lattice parameters.
Performance Filters
Two filters are available to search by stiffness within the unit cell's stress-strain curve: modulus and stress at 25% strain. You can also search by volume fraction to estimate the weight of the lattice.
Simulated Testing
In order to have performance data for thousands of lattices, the library utilizes simulated testing.
Simulations have been developed and validated from physical experiments on a wide cross section of EPU 40 printed lattice pucks.
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Results yield a stress/strain curve and volume fraction for each lattice.
For more details, read Building Carbon's Metamaterials Library.
Because data is based on simulations, final part performance may vary.
Our simulated mechanical response data reasonably matched experimental data on the small set of lattices we tested in a physical setting. However, these tests were performed with ideal, simple parts in a controlled environment. We do not expect the precise numbers shown to accurately describe performance of parts that are more complex or used in less ideal settings. The data like the stress-strain curves shown in Design Engine are best used as a comparative tool in evaluating a lattice’s performance relative to other lattices. Actual lattice behavior depends on specific use and is subject to variation inherent in manufacturing processes and different environments in which products are used. Users should validate lattice behavior in settings specific to their needs.
Modulus
Young's modulus, or modulus of elasticity in compression, is calculated in the linear elastic range of compression. The slope of the stress-strain curve in this range, rise over run, provides a performance metric for how stiff the lattice is before yielding, or buckling. The higher the number, the stiffer the lattice in this range. 
In the example shown, the lattice exhibits 5.54 kPa of stress at 2% strain for a modulus of 277 kPa (a relatively compressible lattice, ie not stiff).
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Stress at 25% Strain
25% strain is a common benchmark to reference stiffness in the plateau range of compression, where the lattice is yielding, or buckling, under stress. This is how much pressure is needed to compress the lattice by 25%. The higher the number, the stiffer the lattice in this range. 
In the example shown, the lattice requires 24 kPa of stress to compress by 25% (a relatively compressible lattice, ie not stiff).
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For more information on what the stress-strain curve can tell you, reference the How to Read Graph section in the Lattice Parameters - Lattice Types lesson.
For more information on stress-strain graphs, reference Stress-Strain Curves﻿.
Volume Fraction
Volume fraction indicates the % of volume the lattice uses out of the total volume of the design space.
Volume fraction is most useful to estimate the weight of your latticed part. Calculate the weight of your lattice with the volume fraction, volume of your design space, and density of the material (available on the technical data sheet for Carbon resins).
Volume fraction can also be an indicator of production cost. Higher volume fractions use more printed material than lower volume fractions.
Note about Foam Density vs Lattice Density
Many successful lattice applications are foam replacements, using lattices for performance gains. In the foam industry, density is often used to indicate the quality and durability of a particular foam. This is not the case with latticed parts. Quality and durability are characteristics of the material the latticed is printed in, not the lattice itself. A low vs high volume fraction in lattice design is not an indication of quality, but is instead a tool to understand the mass of the lattice, relative to the material used. To understand the durability of your lattice, reference the material properties of the printed material.
For more information on volume fraction per lattice type, reference Mass Comparison﻿﻿
Why Lattices Do Not Use Shore Hardness
Shore hardness is measured with a durometer, which uses a small pin as the testing plunger, and provides a unitless measure of hardness via a dial or digital readout. The pin plunger is very small, ranging in diameter between 1.1 - 1.4 mm. As illustrated below, a lattice can miss the measurement entirely as the pin falls in the negative space between struts. Even if the durometer pin hits a strut to get a reading, the pin is too small to get an accurate sense of how the lattice is performing, which relies on how the struts work together as a unit. Testing lattice compression requires a platen or plunger that spans across one unit cell at a minimum, ideally multiple unit cells. 
The pin applies a load to a depth of 0-2.5 mm, which most closely aligns with the modulus measurement used in Design Engine. If you are trying to match a material where you only have shore hardness data to pull from, you can approximate the roughly similar modulus metric via a conversion formula provided below.
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Convert Shore Hardness to Modulus.xlsx
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Note this conversion is approximate and should be considered a rough correlation only. The formula uses A.N Gent's equation for ASTM D2240 Type A durometer hardness.
Qualitative Comparisons
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If you have a particular foam in mind that you are trying to replicate, see the Foam to Lattice Workflow﻿ example below.
Note that combining lattices with skins or using thicker boundary struts than the body of the lattice, can make the structure feel slightly stiffer in performance.
Lattice Parameter Filters
Standard lattice parameters can also be used to filter down results.
Cell Size
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Narrow the cell sizes that appear in search results based on your part geometry and manufacturability. 
Strut Diameter
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Narrow the strut diameters that appear in search results based on your material.
Lattice Type
Lattice Search catalogs lattice types for both tetrahedron mesh and hexahedron mesh scaffold types.
Scaffold Type
Toggle between tet and hex  scaffold type to search per mesh preference.
Hybrids are only available for tet mesh types.
The primary lattice types available will vary to match the selected scaffold type.
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Tet Lattice Types
There are more options than just the five primary tet lattice types available in the Strut Lattice operation.
Two additional tet lattice types appear in the library: Kelvin (Tet) and Star (Tet)
Hybridized lattice types are also available in many combinations
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Hybrid Lattice Types
Hybridized lattices are available using all seven tetrahedron lattice types:
Icosahedral | Kagome | Kelvin (Tet) | Rhombic | Star (Tet) | Tetrahedral | Voronoi
The example here is 1/3 Star and 2/3 Voronoi. The unit cells of each type merge together to create a unique unit cell in the noted proportions. 
Hybrid lattices are named by their components, using the first three letters of each lattice type, followed by their proportions as a percentage.
In this example: StaVor_3366
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Hex Lattice Types
To create a lattice using a Hex Mesh, you must generate the Hex Mesh via the Hex Mesh﻿ operation before you can select and apply unit cell parameters via the Strut Lattice operation.
Gridded hex mesh with equal-sided cuboids
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Lattice Search assumes a gridded Hex Mesh with equal XYZ hexahedron dimensions. 
This equal-sided cuboid is the cell size of the strut lattice unit cell shown in the meta-materials library (MML).
When reviewing lattice performance in the MML, reference the closest approximate cell size to your hex mesh.
Note that when using the apply unit cell option when launching Lattice Search directly from the Strut Lattice operation, the cell size will not be applied, as the cell size of your Hex Mesh will be used. Only the lattice type and strut diameter will carry through.
Your actual hex lattice performance may vary depending on the type of hex mesh﻿ you use and the size and proportions of the hexahedrons in your hex mesh.
Note that there is a Star lattice type available for both tet and hex scaffold types.
Material
Elastomers
The metamaterials library currently catalogs lattices in Carbon's elastomeric materials:
EPU 40 | EPU 41 | EPU 43 | EPU 44 | EPU 45 | EPU 46 | SIL 30
Packaging Not to Scale  |  Use EPU 44 results for EPU 46
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For more guidance and manufacturability information, reference the Lattice Parameters﻿ lesson.
Lattice Search Demo
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Video Text
Measure Part Geometry
• Measure part - using Thickness tool in this example
• Follow guidelines to find a main cell size range
• ~20 mm smallest dimension = ~15 mm max cell size
Strut Lattice - Lattice Search
• Select input mesh
• Select Lattice Search under lattice type
Filter Results
• Adjust modulus for pre-yielding stiffness
• Adjust stress at 25% strain for pre-densification stiffness
• Adjust volume fraction to make your lattice more or less dense
• Adjust to acceptable cell size range for your geometry
• Adjust strut diameter to acceptable range for material
• Include or hide hybrid lattice types
• Select which lattice types to include
• Select materials (currently elastomers)
Browse Results
• Sort Results
• Select lattices to compare details
• Compare up to 6 lattices
   • Compare stress-strain curves in graph view
      • Data may be downloaded as a CSV
   • Compare lattice patterns in model view
      • Sample pucks are 40 x 40 x 20 mm
Select a Lattice
• Select option - applying all unit cell parameters in this example
Generate and Assess Lattice
Apply Options and Solidify
• Adjust advanced options as needed
• Solidify for a printable mesh
Note that using Lattice Search for a zone will only apply the lattice type to the zone, rather than all unit cell parameters. 
When performance data is not available within the metamaterials library, a button to request performance data is available within the Strut Lattice tool.
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Foam to Lattice Workflow
One of the key challenges that designers face when designing with a lattice is not having a clear path to mimic the mechanical performance and aesthetics desired. Searching a vast library can be a daunting task if you don't have specific performance criteria in mind.
A common path in lattice design is to have foam characteristics in mind as a benchmark for finding lattices that perform in a similar capacity. 
Compare to Foams in Library
Carbon tested a cross section of common foams to capture data in the same format as the library's lattice simulation data, to provide a reference point for finding unit cells. For more details on Carbon’s testing and data modeling, reference this white paper.
Filter by Foam
In the materials filter, click on foam to see all foams available in the metamaterials library.
 
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Generic Foam Details
Several of the foams we tested are from broad generic categories. To provide more context, below are the retailer specifications for these foams.
Generic Foam
Common Application
Retailer Specs
Closed Cell Foam (EVA) 
Exercise Mats
EVA Foam "Firm"
Density: 2.0 pcf (0.032 g/cc)
High Density Foam 
Furniture Cushions
EverFlex V54 54 ILD (240 N)
Density: 2.9 pcf (0.046 g/cc)
Latex Foam
Mattresses and Cushions
N28 28 ILD (125 N)
Density: 6 pcf (0.096 g/cc)
Memory Foam 
Mattresses and Cushions
13 ILD (58 N)
Density: 2.5 pcf (0.040 g/cc)
Neoprene Foam 
Gaskets
3 psi to compress 25% (20.7 kPa*)
Density: 10.0 pcf (0.160 g/cc)
Packing Foam 
Packing/Shipping
Y37ch Foam 35 ILD (156 N)
Density: 1.2 pcf (0.019 g/cc)
Rebond Foam
Carpet Padding
90 ILD (400 N)
Density: 8.0 pcf (0.128 g/cc)
* Results of Carbon testing did not match retailer specs. Testing conditions may vary results.
Foam to Lattice Search
1
Filter Foam Performance
Select foam to match
Check the box to compare
Filter modulus range close to foam
Choose a range +/- a couple hundred because the linear elastic range is generally a small part of the data set.
Filter stress at 25% strain range close to foam
Choose a tight range for best results
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Filter Lattice Parameters
Select materials for application
Energy return in example
Select cell size range to suit geometry
Select strut diameter range to suit resin and cell size range
Select volume fraction range to suit weight goals
Optionally filter to preferred lattice types
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Compare Results
Select up to 5 options to compare foam
Highlight foam for clarity
Hover cursor over strain at 50%
Match the closest compression metrics
Closest lattice
Apply unit cell to generate strut lattice
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4
Check Unit Cell Manufacturability
In this example, Voronoi with a 10mm cell size and 0.8mm strut diameter closely matches our high density foam.
Check that the unit cell conforms well to your design space
Verify manufacturability for the unit cell
In this case, the parameters are well within the range of Voronoi's manufacturability in Carbon's DLS production
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For manufacturability information for tet lattices, reference Unit Cell Manufacturability﻿.
Compare to Other Foams
Align Data
If you have your own foam testing data, you may need to align your data to match the format in Design Engine before comparing data.
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Stress - Strain
Data may be in Force (N) - Displacement (mm) units rather than Stress(kPa) - Strain (%). The same curve may appear slightly different when plotted in different units, which can throw off your search results.
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Stress
Divide force by the surface area of the testing apparatus on the sample.
If testing was performed by a plunger, use the plunger surface area. If a platen was used that covers the full sample, use the surface area of the sample.
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Strain
Convert the displacement dimension to a percentage of the sample thickness.
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Plot Curve and Compare to Lattices
Plot stress-strain curve
Plot data points at 2, 4, 6... 60% strain to match Design Engine graphs
Use the cycle 2 curve if you have multiple cycles
Perform a lattice search per the foam to lattice workflow﻿ above
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Generic Foam	Common Application	Retailer Specs
Closed Cell Foam (EVA)	Exercise Mats	EVA Foam "Firm" Density: 2.0 pcf (0.032 g/cc)
High Density Foam	Furniture Cushions	EverFlex V54 54 ILD (240 N) Density: 2.9 pcf (0.046 g/cc)
Latex Foam	Mattresses and Cushions	N28 28 ILD (125 N) Density: 6 pcf (0.096 g/cc)
Memory Foam	Mattresses and Cushions	13 ILD (58 N) Density: 2.5 pcf (0.040 g/cc)
Neoprene Foam	Gaskets	3 psi to compress 25% (20.7 kPa*) Density: 10.0 pcf (0.160 g/cc)
Packing Foam	Packing/Shipping	Y37ch Foam 35 ILD (156 N) Density: 1.2 pcf (0.019 g/cc)
Rebond Foam	Carpet Padding	90 ILD (400 N) Density: 8.0 pcf (0.128 g/cc)
Updated 26 Sep 2024
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