ME 922 Thermoelasticity and Viscoelasticity
Prerequisite: ME 820, MTH 443 (less important).
Instructor: T. J. Pence, 2452EB, 353-3889, pence@egr.msu.edu.
Time and Place: MW 10:20-11:40
in Room 19 of the Natural Resources Building.
Text: The course material is drawn from a variety of
sources. A main text from which I will draw lecture
material on viscoelasticity is:
- Mechanical Response of Polymers: An Introduction, A. S. Wineman
& K. R. Rajagopal, Cambridge University Press, 2000.
This is an easy text to read and the material covers general
viscoelasticity. In particular, it is not limited to polymers
(despite the title).
<>Course Description: This course focuses on the modeling and
analysis of time dependent and thermal dependent effects in solids and
soft matter. The most critical time dependent effect is
viscoelasticity, wherein the mechancial response depends on the rate at
which external processes of mechanical and thermal loading take
place. This includes creep (continuing strain at fixed stress),
and relaxation (change in stress at fixed strain).
Such processes have a great influence on the behavior of: asphalts,
polymers, gels, and soft biogical tissue. In addition, we
shall discuss certain aspects of fluid seepage in highly deformable
porous media, since this is one mechanism giving rise to viscoelastic
behavior, and it is an important consideration in all of the materials
listed above. Among the topics that we shall cover are:<>
- <>Basic aspects of viscoelastic response
- Simple mechanical alanogies in one-dimensioan: Maxwell, Kelvin
&
Voight models
- Linear viscoelastic response in one dimension & superposition
principles
- Relaxation and creep, fading memory
- Constant strain rate processes, constant stress rate processes,
recovery,
- Oscillatory processes, complex viscosity
- Three dimensional response, extension/shear coupling
- Axial load, bending and torsion, correspondence principle
- Boundary value problems, correspondence principle for
quasi-static motion
- Thermal effects, time-temperature superposition
- Dynamical effects and wave propagation
- Poroelastic response of highly deformable media
- Constitutive models based on pressure driven fluid seepage
- Poroelastic boundary value problems, time scales associated with
undrained and drained response
Grading: Grades will be assigned on the basis of a few
homework assignments (35%), a mid-term exam (25%) and a project
(40%). The project will involve independent study of a topic of
interest that relates to this course and reporting on that topic
to the class. The final exam time will be used for the last
couple project
presentations.