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מבוא למכניקת מוצקים עם מיקרו מבנה
Introduction to Mechanics of Solids with Microstructure |
0540-6417-01 | ||||||||||||||||||||||||||||||||
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הקורס יינתן בשפה האנגלית
The course covers the analytical and computational methods to model and simulate mechanical behavior of materials taking their microstructure into account. Multiscale modelling from atomistic level to macrolevel allows to describe and predict effective properties of materials. Nowadays it is highly important for nanostructures, composites, metamaterials, and foams. Also, multiscale methods are highly important for study of fracture and dislocation mechanics, plasticity. This course allows to understand some general concepts and use them to study different problems in mechanics of solids.
הנדסה
0540-6417-01 מבוא למכניקת מוצקים עם מיקרו מבנה
Introduction to Mechanics of Solids with Microstructure
שנה"ל תשע"ז | סמ' א' | ד"ר ברינסקי איגור
Course plan:
1. Introduction to the micro- and nanomechanics. Scale levels. Classification of condensed matter. Structure of solids. Elements of crystallography: crystal lattice, symmetry groups, experimental methods in crystallography. Nanomaterials. Quasicrystals.
2. Nature and types of interatomic bonds. Chemical bond, energy and valence. Types of the bonds: ionic, covalent, metallic, Van-der-Waals.
3. Micromechanical defects in crystals. Point defects. Dislocations. Cracks. Fracture of solids.
4. Empiric description of solids. Potentials of interaction: Lennard-Jones, Stillinger-Weber and REBO, EAM. Force fields.
5. Review of tensor calculus in solid mechanics. Dyads, high-order tensors, dot product, vector product, trace, transpose, coordinates of the tensor.
6. Tensors of stress and strain at macroscopic level. Hook’s law for anisotropic solids.
7. Atomistic foundations of continuum mechanics. Micro-canonical ensembles. Total energy, kinetic energy, pressure, temperature.
8. Molecular statics and dynamics. Verlet and leap-frog integration. Neighbors list. Boundary conditions.
9. Linear deformation of crystal lattice. Cauchy-Born rule. Tensor of stress at microscopic level. Examples: simple crystal lattices.
10. Linear deformation of complex crystal lattice. Nonlinear deformation of simple crystal lattice. Cauchy, Piola, virial, Hardy stress.
11. Dynamics of 1D crystal. Dynamics of 2 and 3-atomic molecule. Dynamics of simple crystal chain.
12. Dynamics of two-atomic crystal. 1D two-atomic chain and its generalization to 2D and 3D crystals. Acoustic and optical spectrum. Dispersion curves. Brillouin zone. Phonons.
13. Nonlinear waves in crystals. Bousinesq equation. Toda’s chain.
14. Atomistic-continuum coupling. Quasicontinuum method. Representative cell method.
Grading:
30% - Home tasks
30% - Research project
40% - Final test
Similar courses:
· Prof. E. Tadmor (University of Minnesota). Multiscale Methods for Bridging Length and Time Scales.
http://www.aem.umn.edu/~tadmor/
· Prof. Wing Kam Liu (Northwestern University). Multi-scale Modeling and Simulation in Solid Mechanics
· Prof. Markus J. Buehler (MIT). Multiscale materials design.
http://professional.mit.edu/programs/short-programs/multiscale-materials-design