Department of Mechanics: Student's corner: Micromechanics of Heterogeneous Materials: Difference between revisions
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==== Lectures ==== | |||
* Week 01: | |||
Introduction, structure of the primal and dual governing equations for scalar potential problems, boundary conditions. | 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. | Variational principles, orthogonality, averages, fluctuating fields, Helmholtz decomposition. | ||
| Line 60: | Line 26: | ||
Voigt-Reuss bounds, dilute approximation, self-consistent method, Mori-Tanaka method, Hashin-Shtrikman-Willis bounds and estimates. | Voigt-Reuss bounds, dilute approximation, self-consistent method, Mori-Tanaka method, Hashin-Shtrikman-Willis bounds and estimates. | ||
==== | ==== Additional course resources {{id name="course-resources" /}}==== | ||
*. Course space in Moodle: https://moodle-ostatni.cvut.cz/course/view.php?id=380\\{{formula}}\gg{{/formula}} Log in as guest | *. Course space in Moodle: https://moodle-ostatni.cvut.cz/course/view.php?id=380\\{{formula}}\gg{{/formula}} Log in as guest | ||
Revision as of 21:38, 9 January 2023
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" /
File:Figures/logolink OP VVV hor barva eng
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/]].