ME 721: Theory of Plasticity


Instructor: Anurag Gupta (ag@)


Schedule: TBA


Grading policy: TBA


Texts: There is no definite text book for the course. I am providing a brief reference list below. Particular reference to these texts is mentioned in the course content.


Books on continuum mechanics:


[1] The mechanics and thermodynamics of continuous media, M. Silhavy, Springer, 1997. (A very rigorous text and the rightful successor to the classic by Truesdell and Noll)


[2] The mechanics and thermodynamics of continua, M. E. Gurtin, E. Fried, and L. Anand, Cambridge Univ. Press, 2010. (A recent text with a comprehensive discussion on basic continuum mechanics, thermoelasticity, and plasticity.)


Books on Plasticity:


[3] Studies in large plastic flow and fracture, P. W. Bridgman, HUP, 1964. (This book mainly deals effect of hydrostatic pressure on plastic flow and fracture of solids. The book concludes with a very informative chapter on introductory plastic theory)


[4] The mechanics of constitutive modeling, N. S. Ottosen and M. Ristinmaa, Elsevier, 2005.


[5] Plasticity theory, J. Lubliner, Dover, 2008.


[6] The mathematical theory of plasticity, R. Hill, OUP, 1998.


[7] Fundamentals of the theory of plasticity, L. M. Kachanov, Dover, 2004.




Course content: (This is from the previous time that I taught this course. I will revise it soon)


1. Preliminaries for the theory: A brief overview of kinematics, balance laws, and dissipation in continuum mechanics. A set of notes on these topics can be found here and here (these notes do not include dissipation). A more detailed treatment of these can be seen in the 3rd chapter of [1].


2. Constitutive theory: Frame-indifference, thermodynamical restrictions, kinematic constraints, material symmetry, material uniformity, material homogeneity. The two books on continuum mechanics mentioned above should suffice for reference.


  1. 3.Uniaxial test. The phenomenon of plasticity


  1. 4.Yield criteria. (Ch. 8 from [4])


5. Simplest theory with isotropy, small deformation, and rate independence. (Ch. from [3], Chs. 74-77 from [2])


Midterm Solution


  1. 6.Elasto-Plastic torsion (Hill, Kachanov)


  1. 7.Axisymmetric problems (Hill, Lubliner)


  1. 8.Slip-line field theory for plane strain elastically rigid perfectly plastic solids. (Hill, Kachanov)

       Slip-line field theory and large-scale continental tectonics as a, P. Tapponnier and P. Molnar, 264, 1976, Nature. [pdf]

       Discontinuous solutions in the theory of plasticity, W. Prager, in Courant Anniversary Volume, 1948. [pdf]

  

  1. 9.Uniqueness and Stability: Papers by R. Hill, [1] [2] [3] [4]

        Example: Plastic column: Papers by Hill and Sewell [1] [2]