ME 6204: Micromechanics of Materials

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