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Mechanics of Dancing Natraja

Mechanics of Dancing Natraja. N. W=mg. What is the origin of the normal reaction?. The origin of the normal reaction is the deformation of the floor. Fiction vs. Reality. Rigidity. vs. How reluctantly the mind consents to reality! ~ Norman Douglas. Brittle and Ductile Solids.

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Mechanics of Dancing Natraja

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  1. Mechanics of Dancing Natraja

  2. N W=mg What is the origin of the normal reaction?

  3. The origin of the normal reaction is the deformation of the floor.

  4. Fiction vs. Reality Rigidity vs How reluctantly the mind consents to reality! ~ Norman Douglas

  5. Brittle and Ductile Solids Brittle: Little or no plastic deformation before fracture, e.g. ceramics Ductile: significant plastic deformation before fracture, e.g. metals

  6. Brittle and Ductile Solids Brittle: Elastic deformation -> Fracture Ductile: Elastic deformation ->Plastic deformation -> Fracture Initial deformation in all solids is elastic

  7. Chapter 10:Elastic, Anelastic and Viscoelastic Beaviour Chapter 11: Plastic deformation Chapter 12: Fracture

  8. All solids initially deform elastically followed by fracture (brittle) or plastic deformation (ductile)

  9. r0 F r0 + dr r0 r

  10. I II III IV Li(3) Be(4) B(5) C(6) Diamond 11.5 289 440 1140 Si(14) 103 Ge(32) 99 Sn(50) 52 Pb(82) 16 Element (Atomic Number) Young’s Modulus in (GPa) Bond strength increases along a period. Bond strength decreases down a group

  11. Elastic Anisotropy Single crystals are elastically anisotropic. Young’s modulus need not be same in different directions of a single crystal. Polycrystalline materials may be isotropic as they may show a value of Young’s modulus which is average of its value over all possible directions. The values shown in the previous slide are all polycrstalline averages

  12. Elastic Anisotropy of Graphite Y100 = 950 GPa Strong covalent bonds Y001= 8 GPa Weak van der Waals bonds

  13. Elastic Anisotropy of Pb Young’s Modulus surface of Pb Y100 = 11 GPa Y110 = 23 GPa Y111 = 38 GPa Ypolycrystal=16 GPa Journal of Physics and Chemistry of SolidsVolume 68, Issue 4, April 2007, Pages 503-510

  14. Structural stiffness: ability of structures to resist elastic deformation on loading ex: spring constant k (F = k x) Material stiffness: Young’s modulus A rod in tension Structural stiffness depends on the material stiffness and structural geometry

  15. Polymer: Low modulus but not brittle Glass, Boron, carbon fibres: Very high modulus but brittle Fibre-reinforced polymer composite (Polymer+Fibre) Much higher modulus than plastics without the brittleness of fibres

  16. Young’s modulus of continuous aligned fibre composite Longitudinal Loading (parallel to the fibres) Transverse loading (perpendicular to the fibres) Isostrain Isostress (Approx.)

  17. Young’s modulus of a GFRP (Glass fibre reinforced polymer) Matrix: Epoxy (Ym=3 GPa) Reinforcement: Glass Fibres (Yf=70 GPa) 70 Yf 60 Young’s modulus (GPa) 50 Upper bound 40 30 Longitudinal 20 Lower bound 10 Ym Transverse 0.2 0.4 0.6 0.8 1 Volume fraction of glass fibres Vf

  18. Rubber Elasticity already covered after chapter 5 Anelasticity and viscoelasticity not in syllabus

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