MECHANICS OF POLYMER SOLIDS
AND FLUIDS
CHE/ME/MSE/TFE 7771
Course coordinators: Dr. A.S. Abhiraman (ChE), Dr. Karl
Jacob (TFE)
Prerequisites:
Undergraduate training in solid and fluid mechanics and
CHE/TFE 4776; 6768; or consent of instructor
Proposed Catalog Description:
Continuum mechanics of solids and fluids; deformation,
yield, fracture and fatigue of anisotropic polymers; experimental response and
constitutive models of non-Newtonian viscous/viscoelastic polymer fluids.
Course Justification:
The learning objectives for the course are as follows:
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.)
We have taken the approach of integrating the mechanics of
solids and fluids in a single course
It is rigorous and yet
explicitly cognizant of the essential empiricism in modeling the behavior of
polymer solids and fluids. The “continuity” of solid- and fluid-like states of
polymers can be best appreciated through this approach. The course materials
have been refined and taught at Georgia Tech for 15+ years as parts of two
courses. Students have historically found the materials in these courses
difficult to assimilate. The problem is often compounded by the absence of a
uniform notation in books and papers. However, this subject is one that will
benefit from the semester-long coverage.
Text: Reference
Texts: Ward: Mechanical properties of solid polymers; Bird et
al.: Dynamics of polymeric liquids - Fluid dynamics; these will be supplemented with papers from
literature.
Topical Outline
1. Analysis
of stresses in a medium
2. Analysis
of deformation in a medium
a.
finite strain
b.
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
4. Symmetry
relations and material constants
Covering
operations for material symmetry; common symmetries in polymeric materials
5. Anisotropic
mechanical behavior of polymers
Consequences
of local and global symmetries in polymer morphology
6. Yield
behavior
Classical
theories of yielding; Hill’s yield criterion; brittle and ductile failures in
polymers; molecular theories of yielding and cold drawing
7. Breaking
phenomena
Classical
theories of fracture; critical strain energy release rates in polymer fracture;
crazing in polymers; molecular theories of fracture in polymers
8. Fatigue
Static
and dynamic fatigue in polymers; empirical formulations; rate theories
9. Framework
of fluid dynamics
Introduction
to viscous Newtonian and non-Newtonian fluids
10. Material functions for
polymer fluids
The
concept of simple fluids; viscometric flows of simple fluids
11. Flow phenomena in
polymer fluids
Experimental
aspects of viscometric functions; flow phenomena on viscoelastic polymer fluids
12. Generalized Newtonian
fluids
Ellis,
power-law and other models; determination of shear viscosity function through capillary flow
13. Linear viscoelastic
fluids
Simple
and generalized Maxwell fluids; frame invariance requirements for constitutive
equations
14. Co-deformational and
corotational models
Maxwell-Oldroyd
and Maxwell-Jaumann fluids;
various modifications
15. Dimensional analysis
vis-a-vis non-Newtonian fluids
Constitutive
equations vis-a-vis dimensionless groups; applications to non-Newtonian viscous
and viscoelastic fluids