Micromechanics of composites
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Welcome to this learning project about Micromechanics of composites!
Learning Project Summary[edit]
- Project code:
- Suggested Prerequisites:
- Time investment: 6 months
- Assessment suggestions:
- Portal:Enegineering and Technology
- School:Engineering
- Department:Mechanical Engineering
- Stream:Applied Mechanics
- Level: Second year graduate
Content summary[edit]
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.
Goals[edit]
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.
Contents[edit]
Learning materials[edit]
- Review of some basic continuum mechanics
- Some basic ideas of micromechanics
- Appendix: Some useful results and proofs
- Proof 1: Tensor-vector identity - 1
- Proof 2: Tensor-vector identity - 2
- Proof 3: Surface and volume integral relation - 1
- Proof 4: Integral of a cross product
- Proof 5: Surface and volume integral relation - 2
- Proof 6: Curl of a gradient - 1
- Proof 7: Curl of a gradient - 2
- Proof 8: Relation between axial vector and displacement
- Proof 9: Relation between axial vector and strain
- Proof 10: Rigid body motion
- Proof 11: More tensor identities
- Proof 12: Relation between volume averaged fields
- Proof 13: Average stress power identity - Cauchy stress
- Proof 14: Average stress power identity - 1st P-K stress
Readings and other resources[edit]
Primary texts[edit]
- 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.
Other reading materials[edit]
- T. Belytschko, W. K. Liu, and B. Moran. Nonlinear Finite Elements for Continua and Structures. John Wiley and Sons, Ltd., New York, 2000.
- J. Bonet and R. D. Wood. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press, 1997.
- F. Costanzo, G. L. Gray, and P. C. Andia. On the definitions of effective stress and deformation gradient for use in MD: Hill's macro-homogeneity and the virial theorem. Int. J. Engg. Sci., 43:533--555, 1985. http://dx.doi.org/10.1016/j.ijengsci.2004.12.002
- P. Chadwick. Continuum Mechanics: Concise Theory and Problems. George Allen and Unwin Ltd., London, 1976.
- M. E. Gurtin. The linear theory of elasticity. In C.~Truesdell, editor, Encyclopedia of Physics (Handbuch der Physik), volume VIa/2, pages 1--295. Springer-Verlag, Berlin, 1972.
- M. E. Gurtin. An Introduction to Continuum Mechanics. Academic Press, New York, 1981.
- R. Hill. Elastic properties of reinforced solids : some theoretical principles. J. Mech. Phys. Solids, 11:357--372, 1963. http://dx.doi.org/10.1016/0022-5096(63)90036-X
- R. Hill. Theory of mechanical properties of fibre-strengthened materials: I. Elastic behavior. J. Mech. Phys. Solids, 12:199--212, 1964. http://dx.doi.org/10.1016/0022-5096(64)90019-5
- R. Hill. On constitutive macro-variables for heterogeneous solids at finite strain. Proc. Royal Soc. Lond. A, 326:131--147, 1972. http://dx.doi.org/10.1098/rspa.1972.0001
- R. Hill. On macroscopic effects of heterogeneity in elastoplastic media at finite strain. Math. Proc. Camb. Phil. Soc, 95:481--495, 1984. http://dx.doi.org/10.1017/S0305004100061818
- S. Nemat-Nasser. Averaging theorems in finite deformation plasticity. Mechanics of Materials, 31:493--523, 1999. http://dx.doi.org/10.1016/S0167-6636(98)00073-8
- S. Nemat-Nasser. Plasticity: A Treatise on Finite Deformation of Heteogeneous Inelastic Materials. Cambridge University Press, Cambridge, 2004.
- P. Perzyna. Constitutive equations for thermoinelasticity and instability phenomena in thermodynamic flow processes. In Stein E., editor, Progress in Computational Analysis of Inelastic Structures: CISM Courses and Lectures No. 321, pages 1--78. Springer-Verlag-Wien, New York, 1993.
- W. S. Slaughter. The Linearized Theory of Elasticity. Birhhauser, Boston, 2002.
- C. Truesdell and W. Noll. The Non-linear Field Theories of Mechanics. Springer-Verlag, New York, 1992.
- T. W. Wright. The Physics and Mathematics of Adiabatic Shear Bands. Cambridge University Press, Cambridge, UK, 2002.
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