Nekin Joshua, The relative density of honeycomb structures is typically estimated by dividing the area of the cell walls by the total area of a unit cell. This is illustrated in the research on the effect of honeycomb relative density on its in-plane properties, where the relative density is calculated based on the overlap areas of the cell walls within the honeycomb structure.

Dear Nekin Joshua Please do recommend my answer if useful.

Determining the relative density of 3D printed cellular structures involves measuring the mass and volume of the structure and comparing it to the mass and volume of a solid block with the same material. Here's a step-by-step guide on how you can find the relative density:

### Materials Needed:

1. 3D printed cellular structure (e.g., honeycomb, double arrowhead)

2. Digital scale

3. Calipers or ruler

4. Solid block or piece of the same material (for comparison)

5. Calculator

### Procedure:

1. **Weigh the 3D Printed Structure:**

- Use a digital scale to measure the mass of the 3D printed cellular structure. Record the mass in grams (g).

2. **Measure Dimensions:**

- Use calipers or a ruler to measure the dimensions of the 3D printed cellular structure. For example, measure the length, width, and height. Record these measurements in centimeters (cm).

3. **Calculate Volume of 3D Printed Structure:**

- If the structure is simple, like a rectangular prism, use the formula: Volume = Length x Width x Height. If the structure is more complex, break it down into simpler shapes and calculate their volumes separately, then add them up.

4. **Calculate Relative Density:**

- Use the formula for density: Density = Mass / Volume. In this case, it's relative density, so you'll be comparing the density of the cellular structure to a solid block made of the same material. Calculate the density for both the cellular structure and the solid block.

- Relative Density = (Density of Cellular Structure) / (Density of Solid Block)

5. **Measure the Solid Block:**

- Weigh the solid block made of the same material as the cellular structure using the digital scale. Record the mass in grams.

- Measure the dimensions of the solid block and calculate its volume using the same method as for the cellular structure.

6. **Calculate Density of Solid Block:**

- Use the formula: Density = Mass / Volume to calculate the density of the solid block.

7. **Compare Relative Density:**

- Compare the relative density of the 3D printed cellular structure to the density of the solid block. A relative density greater than 1 indicates that the cellular structure is denser than the solid block, while a relative density less than 1 indicates it is less dense.

### Note:

- Ensure accurate measurements for both mass and dimensions.

- If the cellular structure has internal voids, make sure to account for them when calculating the volume.

- Consider repeating the measurements and calculations for accuracy.

This method provides a basic understanding of the relative density of the 3D printed cellular structure compared to a solid block. Keep in mind that the actual mechanical properties of the structure will depend on factors such as the specific geometry, material properties, and the 3D printing process used.