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
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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>>http://creativecommons.org/licenses/by/4.0/]].