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# Can you calculate dimensions knowing the volume fraction is 0.2?

## Can you calculate dimensions knowing the volume fraction is 0.2?

(OP)
I am going to model this in a FEM programme (COMSOL), and for computational reasons the symmetry is fully exploited. Picture 1 is a cubic lattice structure, its supposed to be a small part of a major repetitive structure. Picture 2 is picture 1 even further simplified (imagine picture 1 being 3x3x3 unit cells of picture 2). I have been told for this structure, I can calculate the dimensions based the volume fraction of 0.2. Does anyone know how to calculate the dimensions (width, thickness, lenght) of picture 2 knowing that the volume fraction is 0.2?

Picture 1

Picture 2

### RE: Can you calculate dimensions knowing the volume fraction is 0.2?

It's the volume of a cube - the volume of 8 little cubes. So for a unit cube with section thickness t

1^3-8*((1-t)/2)^3=vol_fraction=.2

t=.072

Cheers

Greg Locock

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