ABSTRACT
In this chapter, the authors examine the concepts of stress, strain, constitutive relations, and various forms of energy. This permits us to present the equations of linear elasticity and to consider the question of uniqueness of solutions to these equations. The stresses have been shown for the orthogonal faces, as have the stress vector T(v) . Students have thus found three planes on which the shear stresses are zero. These are the so-called principal planes corresponding to the principal stresses. The set of terms ϵijcontains the implicit assumption that they are expressed as functions of the coordinates in the undeformed state— i.e., the so-called Lagrange coordinates. In order to ensure single-valued, continuous solutions ui, we must impose certain restrictions on ϵij. The rigorous solutions of three-dimensional problems of elasticity are few. Consequently, there is a need to simplify problems so that we can obtain a mathematical solution that is reasonably close to representing the actual physical problem.
