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.

Homogenization via averaging and variational principles, primal-dual equivalence.

Apparent properties, effective properties, principle of up-scaling.

Elementary theory of effective properties: Voigt-Reuss estimates, Voigt-Reuss bounds, laminates.

Fourier transform, Green’s function, statement of the Eshelby problem.

Solution to the Eshelby problem, equivalent inclusion method.

Dilute approximation, self-consistent method, Mori-Tanaka method.

Ensemble (averaging), one- and two-point probability functions, homogeneity, isotropy, and ergodicity, stochastic variational principles.

Voigt-Reuss bounds, Hashin-Shtrikman-Willis variational principles, bounds, and estimates.

Structure of the governing equations of linear elasticity, variational principles, material symmetries.

Voigt-Reuss bounds, dilute approximation, self-consistent method, Mori-Tanaka method, Hashin-Shtrikman-Willis bounds and estimates.

Additional course resources Template:Id name="course-resources" /

• . Course space in Moodle: https://moodle-ostatni.cvut.cz/course/view.php?id=380\\Template:Formula\ggTemplate:/formula Log in as guest
• . Lectures in GitLab: https://gitlab.com/open-mechanics/teaching/d32_hm1_en

Acknowledgments Template:Id name="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/]].