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Lecturer(s)
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Rohan Eduard, Prof. Dr. Ing. DSc.
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Course content
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1) Introduction - heterogeneous media, examples of applications in biomechanics, geomechanics, composite materials. 2) The notion of the scale, reference volume element,, multiscale description, averaging 3) Diffusion in porous media, various approaches, the Darcy law 4) Fluid saturated porous solids, historical remarks, conservation laws, phenomenological theory. 5) Biot continuum, various parameters and the links between them, basic 1D problems 6) Multiphase theory of mixtures, mechano-chemo-electric interactions, extended Darcy law. 7) Introduction to the asymptotic analysis with respect to the scale parameter, 1D continuum. 8) Homogenization method for periodic structures, formal asymptotic expansion technique. 9) Two-scale convergence, "unfolding" metod and its application for perforated and strongly heterogeneous materials. 10) Waves in heterogeneous elastic media, dispersion. 11) Metamaterials: phononic a photonic crystals, band gaps. 12) Multiscale modeling applied in the tissue biomechanics - bones, tissue blood perfusion. 13) Processing and evaluation of material micrograph images for microstructure reconstruction.
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Learning activities and teaching methods
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Lecture, Practicum
- Contact hours
- 52 hours per semester
- Preparation for an examination (30-60)
- 40 hours per semester
- Graduate study programme term essay (40-50)
- 45 hours per semester
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| prerequisite |
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| Knowledge |
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| assumed skills essentials in the mathematical analysis and tensor calculus, basics in PDE |
| assumed skills basics in mechanics, especially in continuum mechanics |
| assumed skills basics in numerical methods employed in computational mechanics |
| znát základy variačního počtu a orientovat se v základních pojmech funkcionální analýzy |
| Skills |
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| formulovat počáteční a okrajové úlohy mechaniky kontinua |
| sestavit algoritmus řešení nelineárních soustav algebraických rovnic |
| řešit počáteční a okrajové úlohy pro lineární obyčejné diferenciální rovnice |
| řešit počáteční a okrajové úlohy pro lineární parciální diferenciální rovnice Fourierovou metodou |
| formulovat bilanční vztahy extenzivních veličin pro kontrolní oblast |
| řešit jednoduché limitní přechody |
| Competences |
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| learning outcomes |
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| Knowledge |
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| be able to use the multiscale approach of modeling |
| to understand multiscale description of deforming porous media saturated by fluids |
| to able to use standard methods of numerical multiscale modeling |
| vysvětlit podstatu metody homogenizace periodických prostředí |
| Skills |
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| to apply the homogenization method for non-complicated examples involving linear diffusion, elastostatics, elastodynamics |
| použít metodu homogenizace pro numerický výpočet efektivních elastických parametrů periodicky heterogenních kompozitů nebo výpočet parametrů jejich tepelné a elektrické vodivosti |
| použít model Biotova typu pro řešení úloh deformace porézního prostředí nasyceného tekutinou |
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| teaching methods |
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| Knowledge |
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| Lecture |
| Practicum |
| Textual studies |
| Skills |
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| Lecture |
| Practicum |
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| Lecture |
| Practicum |
| assessment methods |
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| Combined exam |
| Seminar work |
| Skills |
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| Combined exam |
| Seminar work |
| Competences |
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| Combined exam |
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Recommended literature
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Boer, Reint de. Theory of porous media : highlights in historical development and current state. Berlin : Springer, 2000. ISBN 3-540-65982-X.
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Cioranescu, Doina; Donato, Patrizia. An introduction to homogenization. 1st ed. Oxford : Oxford University Press, 1999.
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Coussy, O. Mechanics of Porous Continua, John Wiley & Sons, 2nd Edition. 1995.
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Hornung, Ulrich. Homogenization and porous media ; Ulrich Hornung. New York : Springer, 1997. ISBN 0-387-94786-8.
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Sanchez-Palencia, E. Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics 127,Springer,. Berlin, 1978.
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