How to find volume fraction of a 3D structure ?

I have a meshed 3D model and I want to find its volume fraction. I also would like to add that the geometry is irregular with varrying breadth. Can you please me how to formulate this. If possible how to also use power law with volume fraction?

[Matt J]

volume as a fraction of what?

[Adeline War]

@Matt J Taking volume fractions of ceramic and metal phase in composites.

Answer 1

[Anshuman]

Hi Adeline,

To find the volume fraction of an irregular 3D meshed model, you can use the following steps:

1. Import the meshed model into MATLAB: Use an appropriate function, such as 'importGeometry' or 'importMesh', to read in the 3D meshed model data. This should create a MATLAB structure that contains the mesh vertex coordinates and connectivity information.
2. Compute the total volume of the mesh: Use the mesh data to compute the total volume of the irregular 3D model. One way to do this is to use the 'tetvolume' function in the MATLAB Mesh Toolbox. This function calculates the volume of each tetrahedron in the mesh and returns the total volume of the mesh.
3. Compute the volume of the solid phase: Once you have the total volume of the mesh, you can use geometric measures or other criteria to identify the solid phase and compute its volume. For example, you could use a threshold based on the distance between the mesh vertices and a reference point to identify the solid phase. To compute the volume of the solid phase, you can use the 'tsearchn' function in the MATLAB Mesh Toolbox to calculate the triangular facets that are partially or fully inside the solid phase, and then compute the volume of these facets.
4. Compute the volume fraction: Once you have computed the volumes of the total mesh and solid phase, you can compute their ratio to obtain the volume fraction of the solid phase in the mesh.

To incorporate a power law with volume fraction, you can use the following formula:

y = a * x ^ b

where 'x' is the volume fraction, 'a' is a constant multiplier, and 'b' is the power law exponent. You can fit this equation to the computed volume fraction data using 'curve fitting' in MATLAB. This allows you to estimate the values of 'a' and 'b' that best fit the data for the meshed model.

Hope it helps!