ME 7203: Advanced Constitutive Relations for Solids

Credit Hours: 3-0-3
Prerequisites: ME 6201 or equivalent, or with the consent of the instructor
Catalog Description: Advanced treatment of constitutive laws for nonlinear behavior of solids. Coupled thermomechanical laws and underlying physical and thermodynamical bases. Behavior of media with underlying substructure.
Textbooks: None
Instructors: David McDowell (ME)
References:
  • J. Lemaitre and J.-L. Chaboche, Mechanics of Solid Materials, Cambridge University Press, 1990.
  • J. Lubliner, Plasticity Theory, Macmillan Publ. Co., 1990.
  • T.L. Hill, Statistical Mechanics: Principles and Applications, Dover, 1987 (originally published by McGraw-Hill, 1956).
  • S.R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics, 1984 (originally published by North- Holland, Amsterdam, 1962).
  • Non-Equilibrium Thermodynamics with Application to Solids, ed. W. Muschik, Springer-Verlag, New York, 1993.
Audience: Advanced graduate students with background in solid mechanics.
Goals: To provide knowledge of state-of-the-art constitutive relations for nonlinear, path-dependent behavior of solids with evolving structure.
Topics:

Week

1-2

3-5

6

7

8

9-10

11-12

13-15

Topic

Course overview, basic elements of constitutive relations

Thermomechanics of solids: statistical thermodynamics, nonequilibrium thermodynamics and constrained equilibrium states

Phenomena and thermodynamics based modeling concepts of:

Thermoelasticity and viscoelasticity

Viscoplasticity

Thermoplasticity and Plasticity as asmptotic rate-independent limits

Internal state variables in viscoelasticity, viscoplasticity
(i) Flow, hardening and internal stresses
(ii) Experimental observations

Finite inelasticity of crystalline solids
(i) Kinematics and constitutive equations for continuum slip
(ii) Polycrystal averaging
(iii) Other materials with structure (e.g. polymers)

Internal state variables for distributed material damage
(i) void nucleation/growth
(ii) creep
(ii) microcracked solids

Grading Scheme:

Nominally four homework sets

 

Project Midterm Exam

 

Oral or written Final Exam