Course detail
Mechanics of Composites
FSI-9MEKAcad. year: 2022/2023
Representative volume element (RVE)concept. Average stress and strain in RVE. Relation between macrofield and microfield parameters. Localization and homogenization. Eigenstrains and eigenstresses. Energy-based approach. Simple estimates on bounds of bulk and shear moduli. Eshelby solution for inclusion. Eshelby's tensor. Application to materials containing microcracks and microvoids. Self-consistent, differential and related averaging metods. Hashin-Shtrikman variational principles. Rate formulation of micromechanical models suitable for material plasticity description. Method of unit cell for solids with periodic microstructure.
Language of instruction
Mode of study
Guarantor
Learning outcomes of the course unit
Prerequisites
In the field of mathematics: Partial differential equations of 2nd order. Elements of variational calculus. Integral and differential calculus.
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
project completed with discussion over the project.
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
D. Gros, T. Seelig, Fracture mechanics with an introduction to micromechanics , 2nd Edition, Springer Heidelberg Dordrecht London New York, ISBN 978-3-642-19239-5 (EN)
J.N. Reddy: Mechanics of Laminated Composite Plates and Shells. CRC Press
S.Nemat-Nasser, M.Hori: Micromechanics. North-Holland
Recommended reading
Classification of course in study plans
- Programme D-IME-K Doctoral 1 year of study, summer semester, recommended course
- Programme D-IME-P Doctoral 1 year of study, summer semester, recommended course
- Programme D-MAT-K Doctoral 1 year of study, summer semester, recommended course
- Programme D-MAT-P Doctoral 1 year of study, summer semester, recommended course
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Statistical homogeneity, average quantities and overall properties. Reciprocal theorem, superposition, Greens function.
3. Overall elastic modulus and compliance tensors. Eigenstrain and eigenstress tensors. Consistency conditions. Eshelbys tensor for special cases. Transformation strains.
4. Estimates of overall modulus and compliance tensors- dilute distribution.
5. Estimates of overall modulus and compliance tensors- self-consistent method.
6. Energy consideration and symmetry of overall elasticity and compliance tensors.
7. Upper and lower bounds for overall elastic moduli. Hashin-Shtrikman variational principle. Part 1.+2.
8. Self consistent, differential and related averaging metods.
9. Solids with periodic microstructure. General properties and field equations. Periodic microstructure and RVE. Periodicity and unit cell.
10. Periodic eigenstrain and eigenstress fields.
11. Mathematical theory of periodic homogenization. Method of asymptotic expansions.
12. Micromechanics of inelastic composite materials.