Micromechanics of composites
Quality resource: this resource has been proposed for featuring on the main page of Wikiversity. |
Welcome to this learning project about Micromechanics of composites!
Learning Project SummaryEdit
- 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 summaryEdit
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.
GoalsEdit
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.
ContentsEdit
Learning materialsEdit
- 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 resourcesEdit
Primary textsEdit
- 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 materialsEdit
- 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.
Learning materialsEditLearning materials and learning projects are located in the main Wikiversity namespace. Simply make a link to the name of the lesson (lessons are independent pages in the main namespace) and start writing! You should also read about the Wikiversity:Learning model. Lessons should center on learning activities for Wikiversity participants. Learning materials and learning projects can be used by multiple projects - and you are encouraged to cooperate with other departments that use the same learning resource. |