Offered Spring, Even Years
| Credit Hours: |
3-0-3 |
| Prerequisites: |
ME 6201 or equivalent; or with the consent of the instructor |
| Catalog Description: |
Fundamental concepts of micromechanics of solids with emphasis on application to composite materials. |
| Textbooks: |
Toshio Mura, Micromechanics of Defects in Solids, 2nd Edition, Kluwer Academic, 1987.
Richard Christensen, Mechanics of Composite Materials, Krieger, 1991. |
| Instructors: |
Jianmin Qu, Iwona Jasiuk, Chris Lynch, David McDowell, Richard Neu, Min Zhou, Charkaoui, Mechanics of Materials Research Group |
| References: |
T. Mura, Micromechanics of Defects in Solids, Martinus Nijhoff Pub., 1987.
S. Nemat-Nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials, North-Holland, 1993.
D. Krajcinovic, Damage Mechanics, North-Holland, 1996. |
| Goals: |
- To introduce unified theories of micromechanics of solids,
- To study the microstructure of materials in the context of continuum theories of mechanics,
- To develop methods and techniques for predicting the mechanical behavior of composite materials.
|
| Audience: |
Advanced graduate students in ME, AE, CE and MSE with background in solid mechanics. |
| Topics: |
Topics of the course include the general theory of eigenstrains, inclusion and inhomogeneity problems, effective properties, inelastic deformation, and damage and failure of engineering composites.
- Review of Fundamental Equations of Elasticity and Plasticity
- Equations of equilibrium
- Compatibility
- Constitutive laws
- Linear elastic (isotropic and anisotropic)
- Plasticity
- Viscoelasticity
- Boundary and interface conditions
- General Theory of Eigenstrains
- Definitions of eigenstrain
- Formal solutions to eigenstrain problems
- Fourier series & integrals representations
- Green's functions representations
- Simulation of defects by eigenstrains
- Dislocations
- 2-D and 3-D cracks
- Inhomogeneities
- Eshelby's solution for an ellipsoidal inclusion
- Equivalent inclusion method
- Interaction between inhomogeneities
- Interfaces
- Effective Properties of Heterogeneous Media
- Random and periodic microstructures
- Probability and random variables
- Spatial descriptors
- Fourier series expansion for periodic structures
- Volume and ensemble averages
- Representative volume element
- Average stresses and average strains
- Tanaka-Mori's theorem
- Upper and lower bounds
- Voigt and Reuss bounds
- Hashin-Shtrikman bounds
- Effective Medium Theories
- Self-consistent methods
- Generalized self-consistent method
- Differential self-consistent method
- Mori-Tanaka method
- Homogenization methods
- Periodic structure
- Perturbation method
- Damage and Failure of Engineering Composites
- Interfaces
- Modeling of imperfect interfaces
- Effects of imperfect interfaces on effective properties
- Fibers
- Fiber fragmentation (shear lag)
- Mechanics of fiber pull-out (push-in)
- Fiber bridging
- Matrix
- Transverse matrix cracks
- Radial cracks
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