Homogenization jupyter notebook for students and professors teaching homogenization

During the COVID period, I supervised two Master’s students for three months, tasking them with developing an educational Jupyter notebook on homogenization. The notebook implements classic mean-field models, including Mori-Tanaka, self-consistent, generalized self-consistent, the four-phase model, Voigt, Reuss, and Hashin-Shtrikman bounds. Although I haven’t promoted it yet, I believe it could be highly beneficial to the community, especially for students new to homogenization.

The notebook focuses on linear elastic inclusions—either spherical or ellipsoidal—that can be isotropic or anisotropic and are randomly dispersed in an isotropic elastic matrix. The four-phase model also allows for the spherical inclusion of an interphase layer. Additionally, there is a separate notebook for viscoelastic homogenization, specifically for linear viscoelastic matrices.

The notebook is available for download on GitHub, along with installation instructions for the required packages. I have successfully tested it on my new MacBook. As with any Jupyter notebook, it is self-explanatory and structured into several key parts:

Part III: Users can build their microstructure of interest and compute the equivalent homogeneous properties for a given filler volume fraction (f).

Part IV: Various models can be compared as f varies from 0 to a chosen maximum (f_max). The output can be saved as text and figures.

Part V: Homogenization calculations can be launched from a text file, allowing for quick results once users are familiar with the notebook.

Part VI: The theoretical models are detailed, with relevant equations and references provided.