A 149 line homogenization code for three-dimensional cellular materials written in MATLAB

Guoying Dong, Yunlong Tang, Yaoyao Fiona Zhao

Research output: Contribution to journalArticleResearchpeer-review

36 Citations (Scopus)


Cellular architectures are promising in a variety of engineering applications due to attractive material properties. Additive manufacturing has reduced the difficulty in the fabrication of three-dimensional (3D) cellular materials. In this paper, the numerical homogenization method for 3D cellular materials is provided based on a short, selfcontained MATLAB code. It is an educational description that shows how the homogenized constitutive matrix is computed by a voxel model with one material to be void and another material to be solid. A voxel generation algorithm is proposed to generate the voxel model easily by the wireframe scripts of unit cell topologies. The format of the wireframe script is defined so that the topology can be customized. The homogenization code is then extended to multimaterial cellular structures and thermal conductivity problems. The result of the numerical homogenization shows that different topologies exhibit anisotropic elastic properties to a different extent. It is also found that the anisotropy of cellular materials can be controlled by adjusting the combination of materials.

Original languageEnglish
Article number011005
Number of pages11
JournalJournal of Engineering Materials and Technology
Issue number1
Publication statusPublished - Jan 2019
Externally publishedYes


  • Cellular material
  • Lattice structure
  • Numerical homogenization

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