ME 7771: Mechanics of Polymer Solids and Fluids

Offered Every Spring


Credit Hours: 3-0-3
Prerequisites: Graduate standing in engineering or equivalent discipline
Catalog Description: Continuum mechanics of solids and fluids; mechanics of deformation of anisotropic polymers; anisotropy and critical phenomena, such as yield, breaking and fatigue; non-Newtonian viscous and viscoelastic behavior of polymer fluids. Crosslisted with CHE, MSE, and PTFE 7771.
Textbooks: Taught in ChE
Instructors: A.S. Abhiraman (ChE), Karl Jacob (PTFE), Mary Lynn Realff (PTFE) (Summer 2004)
Goals:

After completing this course, the student should be able to:

  1. Learn the foundations of mechanics of large deformations in solids and non-Newtonian flow of fluids
  2. Learn the foundations in mechanics for developing structure-property relations in anisotropic bulk polymers
  3. Learn phenomenological continuum constitutive models in polymer fluids and solids
  4. Learn the distinctions between polymers and small molecular materials in critical mechanical phenomena (yield, fracture, fatigue, etc.)
Topics:

  1. Analysis of stresses in a medium
  2. Analysis of deformation in a medium
    1. finite strain
    2. small strain
  3. Linear and non-linear elasticity
  • Constitutive relations for large elastic deformations; strain energy function and its relationship to stress tensor for large deformations; Relationships between continuum and molecular models of rubber elasticity
  • Symmetry relations and material constants
    • Covering operations for material symmetry; common symmetries in polymeric materials
  • Anisotropic mechanical behavior of polymers
    • Consequences of local and global symmetries in polymer morphology
  • Yield behavior
    • Classical theories of yielding; Hills yield criterion; brittle and ductile failures in polymers; molecular theories of yielding and cold drawing
  • Breaking phenomena
    • Classical theories of fracture; critical strain energy release rates in polymer fracture; crazing in polymers; molecular theories of fracture in polymers
  • Fatigue
    • Static and dynamic fatigue in polymers; empirical formulations; rate theories
  • Framework of fluid dynamics
    • Introduction to viscous Newtonian and non-Newtonian fluids
  • Material functions for polymer fluids
    • The concept of simple fluids; viscometric flows of simple fluids
  • Flow phenomena in polymer fluids
    • Experimental aspects of viscometric functions; flow phenomena on viscoelastic polymer fluids
  • Generalized Newtonian fluids
    • Ellis, power-law and other models; determination of shear viscosity function through capillary flow
  • Linear viscoelastic fluids
    • Simple and generalized Maxwell fluids; frame invariance requirements for costitutive equations
  • Co-deformational and corotational models
    • Maxwell-Oldroyd and Maxwell-Jaumann fluids; various modifications
  • Dimensional analysis vis-a-vis non-Newtonian fluids
    • Constitutive equations vis-a-vis dimensionless groups; applications to non-Newtonian viscous and viscoelastic fluids
    Delivery mode (%):

    Lecture

    100

    Grading scheme (%):

    Homework

    10

    Exams

    90