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.
  • 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 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