Modelling of Composite Materials

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 multi-scale homogenization. The students will also become familiar with the CELP software intended for a quick estimate of properties of mutli-phase 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, Self-Consistent method

7. Basic macromechanical models - Mori-Tanaka method, CELP software

8. First order homogenization theory - periodic unit cell, periodic boundary conditions

9. First order homogenization theory - displacement-driven vs stress-driven 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 multi-scale 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. Mori-Tanaka method - randomly distributed spherical inclusions

6. Self-consistent method - randomly distributed spherical inclusions

7. Mori-Tanaka method - unidirectional fibrous composite

8. Self-consistent 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 978-1-84564-682-0.

2. G.J. Dvorak: Micromechanics of Composite Materials, Springer Dordrech Heidelberg New York London, 2013, ISSN 0925-0042, ISBN 978-94-007-4100-3.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Stavební inženýrství - materiály a diagnostika staveb (compulsory course)