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.
Textbook: None
Instructor: 
David McDowell (ME) (Fall 2004)

Goals:

  • To provide knowledge of state-of-the-art constitutive relations for nonlinear, path-dependent behavior of solids with evolving structure.

    • Audience:

  • Advanced graduate students with background in solid mechanics.
    • Week
    Topic
    1-2
    Course overview, basic elements of constitutive relations
    3-5
     
    Thermomechanics of solids: statistical thermodynamics, nonequilibrium thermodynamics and constrained equilibrium states
     
    Phenomena and thermodynamics based modeling concepts of:
    6
    Thermoelasticity and viscoelasticity
    7
    Viscoplasticity
    8
    Thermoplasticity and Plasticity as asmptotic rate-independent limits
    9-10
    Internal state variables in viscoelasticity, viscoplasticity
     
    (i) Flow, hardening and internal stresses
     
    (ii) Experimental observations
    11-12
    Finite inelasticity of crystalline solids
     
    (i) Kinematics and constitutive equations for continuum slip
     
    (ii) Polycrystal averaging
     
    (iii) Other materials with structure (e.g. polymers)
    13-15
    Internal state variables for distributed material damage
     
    (i) void nucleation/growth
     
    (ii) creep
     
    (ii) microcracked solids

    Evaluation:

    Useful 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.

     

    ____________________
    Revised July 2004