Asymmetric Elasticity

Abstract

In this chapter I consider elastic equilibrium under the hypothesis that the stress components need not be symmetric; that is, X _rs ≠ X _sr [and Y _rs ≠ Y _sr ]. The best known books on the theory of elasticity do not in general consider this case, and only a few papers are devoted to it. Somigliana has established some general equations for slightly deformable bodies. Later Bodazewski has considered the problem, also applying it to hydrodynamics. However, the results of these authors are based on an expression of the work done by the internal contact forces [Somigliana] or on linear stress-strain relations [Bodazewski] which do not seem acceptable. The cause of asymmetry of X _rs may be the presence of body moments. This means that the body forces acting upon an infinitesimal element are reducible to a force applied at a point of the element and a couple, as happens, for example, in the presence of magnetic forces. This case is considered the most interesting one.