Department of Mechanics: Student's corner: Micromechanics of Heterogeneous Materials: Difference between revisions

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=== Lectures ===
=== Lectures ===
* Week 01:  
* 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.
* Week 02: Homogenization via averaging and variational principles, primal-dual equivalence.
* Week 02: Apparent properties, effective properties, principle of up-scaling.
* Week 02: Elementary theory of effective properties: Voigt-Reuss estimates, Voigt-Reuss bounds, laminates.
* Week 02: Fourier transform, Green’s function, statement of the Eshelby problem.
* Week 02: Solution to the Eshelby problem, equivalent inclusion method.
* Week 02: Dilute approximation, self-consistent method, Mori-Tanaka method.
* Week 02: Ensemble (averaging), one- and two-point probability functions, homogeneity, isotropy, and ergodicity, stochastic variational principles.
* Week 02: Voigt-Reuss bounds, Hashin-Shtrikman-Willis variational principles, bounds, and estimates.
* Week 02: Structure of the governing equations of linear elasticity, variational principles, material symmetries.
* Week 02: Voigt-Reuss bounds, dilute approximation, self-consistent method, Mori-Tanaka method, Hashin-Shtrikman-Willis bounds and estimates.


* Week 02:
=== Additional course resources ===
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 {{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
*. Lectures in GitLab: https://gitlab.com/open-mechanics/teaching/d32_hm1_en
*. Lectures in GitLab: https://gitlab.com/open-mechanics/teaching/d32_hm1_en


==== Acknowledgments {{id name="acknowledgments" /}}====
==== Acknowledgments ====


[[image:figures/logolink_OP_VVV_hor_barva_eng||alt="image"]]
[[image:figures/logolink_OP_VVV_hor_barva_eng||alt="image"]]

Revision as of 21:40, 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.
  • Week 02: Homogenization via averaging and variational principles, primal-dual equivalence.
  • Week 02: Apparent properties, effective properties, principle of up-scaling.
  • Week 02: Elementary theory of effective properties: Voigt-Reuss estimates, Voigt-Reuss bounds, laminates.
  • Week 02: Fourier transform, Green’s function, statement of the Eshelby problem.
  • Week 02: Solution to the Eshelby problem, equivalent inclusion method.
  • Week 02: Dilute approximation, self-consistent method, Mori-Tanaka method.
  • Week 02: Ensemble (averaging), one- and two-point probability functions, homogeneity, isotropy, and ergodicity, stochastic variational principles.
  • Week 02: Voigt-Reuss bounds, Hashin-Shtrikman-Willis variational principles, bounds, and estimates.
  • Week 02: Structure of the governing equations of linear elasticity, variational principles, material symmetries.
  • Week 02: Voigt-Reuss bounds, dilute approximation, self-consistent method, Mori-Tanaka method, Hashin-Shtrikman-Willis bounds and estimates.

Additional course resources

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.

File:Figures/CC BY 4 0

This work is licensed under the [[Creative Commons Attribution 4.0 International License>>http://creativecommons.org/licenses/by/4.0/]].

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