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Homogenization code for 3D lattice structure

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homogenization

Please cite the following article if you use this code in your publications:

Dong G, Tang Y, Zhao Y. A 149 Line Homogenization Code for Three-Dimensional Cellular Materials Written in matlab. ASME. J. Eng. Mater. Technol. 2018;141(1):011005-011005-11. doi:10.1115/1.4040555.

Homogenization code for 3D lattice structure. For more information you can visit http://www.intralatticepro.com/

alt text

"homo3d.m" is to calculate the homogenized material property of 3d lattice structures.

"GenerateVoxel.m" is to generate the voxel model for homo3d.m.

"visual.m" is to plot the 3D Young's modulus surface indicating E along all directions.


To use homo3d.m :

CH = homo3D(lx,ly,lz,lambda,mu,voxel);

% lx       = Unit cell length in x-direction.

% ly       = Unit cell length in y-direction.

% lz       = Unit cell length in z-direction.

% lambda   = Lame's first parameter for solid materials.

% mu       = Lame's second parameter for solid materials.

% voxel    = Material indicator matrix.

% lambda = vE/(1+v)(1-2v), mu = E/2(1+v), E is Young's modulus, v is Poisson's ratio


To use GenerateVoxel.m :

[voxel,Density] = GenerateVoxel(n,address,radius);

% n       = the number of voxel along each axis.

% address = the file location of wireframe.

% radius  = the radius of the lattice structure.

% Density = the relative density of the lattices.

The predifined wireframe file can be found in the topology folder.

The length of the unit cell is 1.


To use visual.m :

visual(CH);

Example:


[voxel,Density] = GenerateVoxel(40,'topology/grid.txt',0.1);

CH = homo3D(1,1,1,115.4,79.6,voxel);

visual(CH)

% the topology is 'grid', the model has 40 voxels along each axis.

% the radius is 0.1, the length of the unit cell is 1 as defined.

% lambda = 115.4, mu = 79.6, whcih is equivalent to E = 200, v= 0.3.

The result is:


Density = 8.5%

CH =

7.1876    0.3875    0.3875    0.0000   -0.0000    0.0000

0.3875    7.1876    0.3875   -0.0000    0.0000    0.0000

0.3875    0.3875    7.1876   -0.0000   -0.0000   -0.0000

0.0000   -0.0000   -0.0000    0.1489    0.0000    0.0000

0.0000    0.0000   -0.0000    0.0000    0.1489   -0.0000

0.0000    0.0000   -0.0000    0.0000   -0.0000    0.1489
    

The Young's modulus surface:

alt text

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