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/
"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:
