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  • Print publication year: 2008
  • Online publication date: June 2012

Chapter 2 - Elasticity and Viscoelasticity

Summary

Introduction

Elasticity deals with elastic stresses and strains, their relationship, and the external forces that cause them. An elastic strain is defined as a strain that disappears instantaneously once the forces that cause it are removed. The theory of elasticity for Hookean solids – in which stress is proportional to strain – is rather complex in its more rigorous treatment. However, it is essential to the understanding of micro- and macromechanical problems. Examples of the former are stress fields around dislocations, incompatibilities of stresses at the interface between grains, and dislocation interactions in work hardening; examples of the latter are the stresses developed in drawing, and rolling wire, and the analysis of specimen–machine interactions in testing for tensile strength. This chapter is structured in such a way as to satisfy the needs of both the undergraduate and the graduate student. A simplified treatment of elasticity is presented, in a manner so as to treat problems in an undergraduate course. Stresses and strains are calculated for a few simplified cases; the tridimensional treatment is kept at a minimum. A graphical method for the solution of two-dimensional stress problems (the Mohr circle) is described. On the other hand, the graduate student needs more powerful tools to handle problems that are somewhat more involved. In most cases, the stress and strain systems in tridimensional bodies can be better treated as tensors, with the indicial notation.

Suggested reading
Fung, Y. C.. A First Course in Solid Mechanics, 2nd. ed. Upper Saddle River, NJ: Prentice Hall, 1997.
Huntington, H. B.. The Elastic Constants of Crystals. New York, NY: Academic Press, 1958.
Kelly, A. and Groves, G. W.. Crystallography and Crystal Defects. Reading, MA: Addison-Wesley, 1970.
Lemaitre, J., and Chaboche, J.-L.. Mechanics of Solid Materials. Cambridge, U.K.: Cambridge University Press, 1990.
Love, A. E. H.. The Mathematical Theory of Elasticity. New York, NY: Dover, 1952.
McClintock, F. A. and Argon, A. S., eds. Mechanical Behavior of Materials. Reading, MA: Addison-Wesley, 1966.
Nye, J. F.. Physical Properties of Crystals. London: Oxford University Press, 1957.
Simmons, G. and Wang, H.. Single Crystal Elastic Constants. Cambridge, MA: MIT Press, 1971.
Sokolnikoff, I. S.. Mathematical Theory of Elasticity, 2nd ed. New York, NY: McGraw-Hill, 1956.
Timoshenko, S. and Goodier, J. N.. Theory of Elasticity. New York, NY: McGraw-Hill, 1951.
Treloar, L. R. G.. The Physics of Rubber Elasticity, 3d ed. Oxford, U.K.: Clarendon Press, 1975.