Department of Mechanics: Student's corner: Micromechanics of Heterogeneous Materials

Lectures

• Week 01: Introduction, structure of the primal and dual governing equations for scalar potential problems, boundary conditions.
• Week 02: Variational principles, orthogonality, averages, fluctuating fields, Helmholtz decomposition.
• Week 03: Homogenization via averaging and variational principles, primal-dual equivalence.
• Week 04: Apparent properties, effective properties, principle of up-scaling.
• Week 05: Elementary theory of effective properties: Voigt-Reuss estimates, Voigt-Reuss bounds, laminates.
• Week 06: Fourier transform, Green’s function, statement of the Eshelby problem.
• Week 07: Solution to the Eshelby problem, equivalent inclusion method.
• Week 08: Dilute approximation, self-consistent method, Mori-Tanaka method.
• Week 09: Ensemble (averaging), one- and two-point probability functions, homogeneity, isotropy, and ergodicity, stochastic variational principles.
• Week 10: Voigt-Reuss bounds, Hashin-Shtrikman-Willis variational principles, bounds, and estimates.
• Week 11: Structure of the governing equations of linear elasticity, variational principles, material symmetries.
• Week 12:: Voigt-Reuss bounds, dilute approximation, self-consistent method, Mori-Tanaka method, Hashin-Shtrikman-Willis bounds and estimates.

Additional course resources

• μFEA.jl library > Develop branch
• Simple Python-based implementation

Acknowledgments

The first version of the course materials was prepared with the support of the European Social Fund and the State Budget of the Czech Republic under project No. CZ.02.2.69/0.0/0.0/16_018/0002274.

This work is licensed under the Creative Commons Attribution 4.0 International License .