ΜΥ1100 ADVANCED MECHANICS OF MATERIALS (ELECTIVE COURSE 2)

ΜΥ1100 ADVANCED MECHANICS OF MATERIALS (ELECTIVE COURSE 2)

Course Information

Course Outline

Course Category
Course Type
Secretary Code
Semester
Διάρκεια
ECTS Units
Sector

Instructor

Undergraduate
Elective Course 2
ΜΥ1100
8th (Spring)
5 hours/week
6
Mechanics Materials and Manufacturing Processes

Agoras Michalis

Course Category: Undergraduate
Course Type: Elective Course 2
Secretary Code: ΜΥ1100
Semester: 8th (Spring)
Duration: 5 hours/week
ECTS Units: 6
Sector: Mechanics, Material and Manufacturing Processes

Instructor: Agoras Michalis

Aim

This course serves as an introduction to the fundamental principles and methods of the Theory of Composite Mateirials. Special emphasis is placed on the application of well-known analytical solutions to composite materials of practical and technological interest, including estimates of the Hashin￾Shtrikman type which are suitable for particulate microstructures and the self-consistent estimates which are appropriate for polycrystalline materials.

Syllabus
Basic concepts and definitions. Convex funtions and the Legendre-Fenchel transform. Constitutive behavior of materials: elasticity, viscoplasticity, plasticity. Material symmetries (anisotropy): orthotropy, transverse isotropy, isotropy.
Static equilibrium of heterogeneous materials: field equations and the classical variational principles. The homogenization problem: the concept of the representative volume element (RVE), periodic and random microstructures, definition of the homogenized (or macroscopic) behavior of composites.
The classical Voigt and Reuss bounds. Some exact solutions: simple and hierarchical laminates, Hashin‘ s composite sphere and cylinder assemblage microstructures.
Eshelby’ s problem: an ellipsoidal, linear elastic particle in an infinite linear elastic matrix. The Hashin-Shtrikman
method and the Hashin and Shtrikman bounds for composite materials with statistically isotropic phase distributions. Generalizations (Willis) of the Hashin-Shtrikman method to materials with anisotropic (“ellipsoidal”) phase distributions. Bounds and estimates for linear composites with random phase distributions: ellipsoidal, spheroidal, spherical, fibrous and lamellar microstructures.
Polycrystalline (granular) microstructures: the self-consistent estimate.
Literature

Suggested Literature:

  • Ponte Castaneda, P., Heterogeneous Materials, Lecture Notes, 2005.
  • Willis, J.R., Mechanics of Composite Materials, Lecture Notes, 2002.
  • Milton, G. W., Theory of Composites, Cambridge University Press, 2002.
  •  Christensen, R. M., Mechanics of Composite Materials, New York: Wiley-Interscience, 1979.
  • Torquato, S., Random Heterogeneous Materials: Microstructure and Macroscopic Properties,
    Springer, 2002.

Related Academic Journals:

  • Journal of the Mechanics and Physics of Solids
  • International Journal of Solids and Structures
  • Advances in Applied Mechanics
Teaching Language

Greek

Teaching Method

Lectures

Student Performance Evaluation

 

 

Written Final Exams50%
Written Homeworks30%
Oral Presentation of a team project20%
Workload (in hours)
ΔActivitySemester Workload
Lectures70
Homeworks35
Study and Analysis of bibliography45
Course total (25 hours per
credit unit) 		150