Encyclopedia of Physics, Volume 6: Elasticity and Plasticity

The theory of elasticity is concerned with the mechanics of deformable bodies which recover their original shape upon the removal of the forces causing the deformation. The first discussions of elastic phenomena occur in the writings of Hooke (1676) but the first real attempts to construct a theory of elasticity using the continuum approach, in which speculations on the molecular structure of the body are avoided and macroscopic phenomena are described in terms of field variables, date from the first half of the eighteen century1. Since that time a tremendous amount of scientific effort has been devoted to the study of the mathematical theory of elasticity and its applications to physics and engineering. The sheer volume of the published work in the subject makes it quite impossible for an author to cover the entire subject at all adequately within the compass of a single book. The present article has a much more modest aim than that: It tries to give a brief survey of certain parts of the basic theory of elasticity with sufficient discussion of special problems to give some indication of the mathematical techniques available for the solution of such problems. Even within that limited framework there are notable omissions; for example, nothing is said about such an important technological topic as the theory of elastic stability or about such a basic topic as the calculation of the elastic constants of a crystal- by the theory of crystal lattices.