Modelling of Composite Materials
Code  Completion  Credits  Range  Language 

132MKOM  KZ  4  2P+1C  Czech 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mechanics
 Synopsis:

The course introduces the theory of homogenization which allows prediction of effective properties of heterogeneous materials by exploiting both classical micromechanics and numerical modeling of periodic structures. Grounding on the theory of elasticity the students will become familiar with the behavior of general anisotropic materials. Application of theoretical formulations is illustrated on several examples of heterogeneous structures encountered in civil as well as mechanical engineering. Such structures include wood, masonry, asphalt mixtures, fibrous composites, metal foams, etc. Determination of effective elastic (Hooke's law) will be accompanied by homogenization of parameters governing various mass transport processes assuming steady state heat flow (Fourier's law, coefficient of thermal conduction) and moisture (Fick's law, coefficient of diffusion). These basic concepts will be eventually presented in the framework of multiscale homogenization. The students will also become familiar with the CELP software intended for a quick estimate of properties of mutliphase material system.
 Requirements:

PRPE, SM3
 Syllabus of lectures:

1. Basic equations of linear elasticity, tensor notation, material symmetry
2. Principles of volume averaging, simplified homogenization approaches
3. Basic energy principles
4. Introduction to micromechanics  representative volume element, concentration (localization) factors
5. Eshelby tensor, transformation inclusion problem
6. Basic macromechanical models  Dilute approximation, SelfConsistent method
7. Basic macromechanical models  MoriTanaka method, CELP software
8. First order homogenization theory  periodic unit cell, periodic boundary conditions
9. First order homogenization theory  displacementdriven vs stressdriven loading conditions
10. Periodic boundary conditions in commercial software
11. Homogenization of transport processes
12. Application of homogenization in the solution of practical problems
13. Introduction to multiscale modeling
 Syllabus of tutorials:

1. Basic equations of linear elasticity, tensor notation, material symmetry
2. Spring models
3. Unidirectional fibrous composite  drawbacks of basic rules of mixture
4. Evaluation of concentration factors  dilute approximation
5. MoriTanaka method  randomly distributed spherical inclusions
6. Selfconsistent method  randomly distributed spherical inclusions
7. MoriTanaka method  unidirectional fibrous composite
8. Selfconsistent method  unidirectional fibrous composite
9. Effective coefficient of thermal expansion, conductivity and diffusion
10. Review
11. First order homogenization
12. Test
13. Preparation for exam
 Study Objective:

The objective is to extend the basic knowledge provided by the theory of elasticity towards the analysis of heterogeneous materials. The course will introduce basic analytical and numerical micromechanical models used in the theory of homogenization thus moving beyond the application of classical rules of mixture. One of the goals is to bring the basic stiffness parameters and parameters describing the mass transport to the same footing.
 Study materials:

1. M. Šejnoha, J. Zeman: Micromechanics in practice, WIT Press, Southampton, Boston, 2013, ISBN 9781845646820.
2. G.J. Dvorak: Micromechanics of Composite Materials, Springer Dordrech Heidelberg New York London, 2013, ISSN 09250042, ISBN 9789400741003.
 Note:
 Timetable for winter semester 2024/2025:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri  Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans:

 Stavební inženýrství  materiály a diagnostika staveb (compulsory course)