Properties of Lattice Structures Under Compression
October 2019-November 2019
The purpose of this experiment is to determine the compressive strength and failure mode of 7 different lattice structures generated via nTopology software. All 7 lattice cubes are printed with Formlabs Flexible Resin and crushed using an Instron 8801 machine. The results of this experiment determine which lattice structure is most suited for use in compressive applications such as latticed shoe midsoles.
Theory
Compressive Stress versus Strain curves are used to analyze the compressive strength of
materials when they are placed under a normal compressive load. Results of
such tests can include the compressive yield stress and compressive modulus of elasticity. In this
experiment, a compression test will be used to generate compressive stress versus strain curves
for seven 1.5” x 1.5” cubes filled with different types of lattices generated using Ntop software. The stress-strain curves will be used to first determine the hardness of each lattice through determination of the Young's Modulus and next to determine the maximum load it can withstand through the Yield Strength of each lattice.
Determination of the failure mode of each lattice is important to understand the method at which the structure will crush under compression. In this experiment, certain types of failure include shear failure, defined as a slip due to insufficient presence of resistance to shear force, and crushing that occurs when lattice cells crush directly downwards in response to vertical force. Certain failure modes may be more or less desirable depending on their application. For example, crushing is more desirable than shearing in a latticed shoe midsole, since a shear failure mode can lead to injuries such as stress fracture.
Methods
In this experiment, each lattice sample is placed into the Instron 8801 machine using a 10kN load cell. Compressive load is applied at a constant rate of 0.5mm/sec for 5 and a half minutes or until critical failure. Stress versus strain data is recorded, and compression of each sample is recorded using an iPhone.
Lattice Samples
Hover over the photos to see the correspondence between sample number and type of lattice. Note that Sample 4 (Octet Lattice) printed such that the cube is essentially a solid block of resin, which causes it to yield inaccurate results during testing.
Body Centered Cubic (BCC)
Re-Entrant
Isotruss
Octet
Diamond
Kelvin Cell
Truncated Octahedron
Sample 1 Failure - BCC
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The BCC lattice has been studied in depth in the latticed sneaker midsole industry, however results of the experiment show that it is insufficient for our purposes. Though the sharp angles at the sides of each cell provide enough resistance to shear breakage, the joints tend to buckle due to a lack of angular space for ligaments to bend to their full extend. The resulting failure mode causes the BCC lattice to crush past the point of restoration, which is not optimal for the use in a sneaker midsole.
Sample 2 Failure - Re-Entrant
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Failure of the Re-Entrant lattice shows apparent "bow-tie" shapes that fit into one another during compression. The vertical struts tend to snap under compression, though they provide an original resistance to compressive force and therefore allow the lattice to endure large forces before failure. Post compression, the re-entrant lattice was able to go back to its original shape, held up by the remaining vertical struts that were not broken.
Sample 3 Failure - Isotruss
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The Isotruss lattice largely consists of vertical and horizontal struts that tend to snap under compression. The vertical force causes the sides of the cubic cell to snap and protrude from the structure at different directions, which creates a wavy pattern on the outside corners. The waviness puts the horizontal struts in direct tension or compression, adding extra forced (non-vertical) onto the structure. Therefore, vertical compression is translated in other directions in the lattice and ultimately causing destruction of the structural integrity of the lattice. The structure is completely destroyed beyond repair after compression, and is therefore not appropriate for use in a latticed sneaker midsole.
Sample 5 Failure - Diamond
The diamond lattice underwent the least breakage under compression and was able to rebound into its original shape post compression. Although some of the ligaments were damaged or broken, it is able to undergo comression again after the first test. It does not have any horizontal or vertical beams, which eliminates the opportunity for shear failure. This lattice was clearly the most suited for use in a sneaker midsole.
Sample 6 Failure - Kelvin Cell
The Kelvin Cell had major diagonal shear failure, since there was little to no angle for the components of the unit cell to bend into. The direct force applied to the small diamond feature that connects one unit cell to the next causes failure in one of the two top lines making up the peaks of the diamond. Whichever of the two lines failed first caused a domino effect of failure in a perfect diagonal, shearing the structure at 45 degrees. Clearly this total failure proves that the Kelvin Cell is not appropriate for use in a sneaker midsole.
Sample 7 Failure - Truncated Octahedron
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The truncated octahedron, like the Kelvin Cell, does not have a large enough angle among the unit cells for the components to bend into under compression. The presence of horizontal and vertical struts in the structure causes horizontal tension and vertical strain leading to strut snapping due to the inability to bend the ligaments to the appropriate angle. The cube therefore bends into an "S" shape, putting certain struts into large amounts of tension causing snap. This is seen in the red lines on the above images.
Total Stress Strain Results
Analysis of the generated stress versus strain plots of each of the seven latticed cubes
shows that each of the lattices react to compression in a similar way that un-latticed materials do.
In each of the full plots of the individual lattices save sample four, there is a clear linear elastic
region of the plot. This is followed by a relatively straight region signifying the perfectly plastic
region in which the material deforms without an increase in the applied load. Next, there is a
portion of each of the graphs where the amount of stress required to cause deformation drops
significantly, which is shown by a steep negative slope. This is finally followed by a region in
which the specimen becomes so flat that it offers increased resistance to shortening for increased
load, which is shown by a flat or positive slope of the graph. The fact that there was no snapping
or point of yield indicates the ductility of the lattices, which is most likely accountable to the
characteristics of Formlabs flexible resin.
The uncharacteristic “unfinished” quality of the graph of sample four, the octet lattice, is
accountable by the fact that the density of the lattice was very thick, and turned out to be
essentially a solid block of material rather than a lattice. This causes its extremely high elastic
modulus, and its lack of a portion of its compressive stress versus strain plot in which the slope is
negative. In other words, the block never yielded under pressure, and the results reflect that.
Analyzing the stress-strain curve below, the lattice with the highest yield strength and corresponding modulus
of elasticity is sample three, which employs the isotruss lattice. The lowest yield strength and
corresponding modulus of elasticity are from sample 1, employing the Body Centered Cubic
lattice. Such results imply that the best acting lattice would be the isotruss lattice, given that its
calculated modulus of elasticity and yield strength is highest. In viewing the true results shown
by the failure mode tests, however, the isotruss lattice was one of the worst acting lattices in
compression, employing multiple failure modes such as waviness and slip planes. The vertical
trusses involved in the isotruss also proved to be faulty, as they tended to snap off after
compression.
Curiously, the lattice with the least visible destruction after compression was sample five
which employed the diamond lattice. The diamond lattice displayed the second to lowest values
of yield strength and Young's modulus, yet the results of compression show that it was the most
likely to retain its shape post compression, and did not undergo many instances of failure such as
shearing or buckling.
Mechanical Properties of Each Lattice
The following results are calculated through analysis of the stress strain curves for each lattice.
Conclusions
The outcomes from this experiment show that the diamond lattice is the most appropriate lattice for use in compressive applications such as for use in a latticed shoe midsole. This is due to the fact that the diamond lattice is the only lattice left completely intact after compressive testing. The results of these tests must be taken with a grain of salt, however, due to the fact that each of the lattices were only tested once. Moving forward, more reliable testing evidence could be made if the tests were repeated multiple times to ensure the presence of breakage and slip planes within the structures are due to lattice type and not due to print defects.
References
“8801 (100kN) Fatigue Testing Systems.” Instron ,
www.instron.us/products/testing-systems/dynamic-and-fatigue-systems/servohydraulic-fati
gue/8801-floor-model.
Goodno, Barry J., and James M. Gere. Mechanics of Materials . 9th ed., Cengage Learning,
2018.
Khlystov, Nikita. “Uniaxial Tension and Compression Testing of Materials.” MIT , 2013,
web.mit.edu/dlizardo/www/UniaxialTestingLabReportV6.pdf.
Lei, Hongshuai, et al., “Evaluation of Compressive Properties of SLM-Fabricated
Multi-Layer Lattice Structures by Experimental Test and μ-CT-Based Finite Element
Analysis.” Materials & Design , Elsevier, 1 Mar. 2019,
www.sciencedirect.com/science/article/pii/S0264127519301224 .