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

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No highlighting permalink download example as JSON Could not load include file geometry.sty at line 4 column 42 Could not load include file inputenc.sty at line 5 column 28 Could not load include file natbib.sty at line 6 column 29 Could not load include file graphicx.sty at line 7 column 22 Could not load include file hyperref.sty at line 8 column 84 Could not load include file fancyhdr.sty at line 9 column 22 Could not load include file pdfpages.sty at line 10 column 22 Could not load include file amsmath.sty at line 11 column 21 Could not load include file amsfonts.sty at line 12 column 22 Skipped '\pagestyle{fancy}' at line 14 column 18 Skipped '\fancyhf{}' at line 15 column 11 Skipped '\chead{D32\_MHM1\_EN | Micromechanics of Heterogeneous Materials I (Analytical Methods)}' at line 16 column 89 Skipped '\rfoot{\thepage}' at line 17 column 17 Skipped '\bibliographystyle{elsarticle-harv}' at line 20 column 36 Skipped '\itemsep=0pt' at line 32 column 30 Skipped '\begin{description}' at line 32 column 20 Skipped '\end{description}' at line 57 column 18 Skipped '\itemsep=0pt' at line 61 column 26 Skipped '\vfill' at line 66 column 7 The course encompasses the essentials of analytical methods for multiscale modeling of heterogeneous materials. In the standard format of 12 weekly lectures of 1 hour and 40 minutes, we will cover the following topics:

Introduction, structure of the primal and dual governing equations for scalar potential problems, boundary conditions.

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.

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/]].