Micromechanics of composites

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Welcome to this learning project about Micromechanics of composites!

• Project code:
• Suggested Prerequisites:
  • Introduction to Elasticity
  • Continuum mechanics
• Time investment: 6 months
• Assessment suggestions:
• Portal:Enegineering and Technology
• School:Engineering
• Department:Mechanical Engineering
• Stream:Applied Mechanics
• Level: Second year graduate

This course is the micromechanics of composite materials. The purpose is to show you ways in which micromechanics may be used to determine the effective properties of composites.

This learning project aims to

• Show you some of the fundamental theorems in the micromechanics of composites.
• Give you a feel for how the theory can be used to determine the effective properties of composites.
• Give you an idea about numerical approaches based on the theory.

1. Review of some basic continuum mechanics
   1. Conservation of mass
   2. Balance of linear momentum
   3. Balance of angular momentum
   4. Balance of energy
2. Some basic ideas of micromechanics
   1. The RVE and governing equations
   2. Infinitesimal deformations
      1. Average strain in a RVE
      2. Average displacement in a RVE
      3. Average stress in a RVE
      4. Average stress power in a RVE
   3. Finite deformations
      1. Average deformation gradient in a RVE
      2. Average velocity gradient in a RVE
      3. Average stress in a RVE
      4. Average stress power in a RVE
3. Appendix: Some useful results and proofs
   1. Proof 1: Tensor-vector identity - 1
   2. Proof 2: Tensor-vector identity - 2
   3. Proof 3: Surface and volume integral relation - 1
   4. Proof 4: Integral of a cross product
   5. Proof 5: Surface and volume integral relation - 2
   6. Proof 6: Curl of a gradient - 1
   7. Proof 7: Curl of a gradient - 2
   8. Proof 8: Relation between axial vector and displacement
   9. Proof 9: Relation between axial vector and strain
   10. Proof 10: Rigid body motion
   11. Proof 11: More tensor identities
   12. Proof 12: Relation between volume averaged fields
   13. Proof 13: Average stress power identity - Cauchy stress
   14. Proof 14: Average stress power identity - 1st P-K stress

• S. Nemat-Nasser and M. Hori, 1993, Micromechanics: Overall Properties of Heterogeneous Materials, North-Holland.
• G. W. Milton, 2002, The Theory of Composites, Cambridge University Press.
• S. Torquato, 2002, Random Heterogeneous Materials, Springer.

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