Remarks on a Question of Ericksen Concerning Elastostatic Fields of Saint-Venant Type

In an effort to understand better the relationship between approximate theories —such as those for thin rods—and the three-dimensional theory of elasticity, Ericksen [1]–[3] has recently suggested a reconsideration of Saint-Venant's problem for elastic cylinders with traction-free lateral surfaces. Among the various questions raised in [1]–[3], one concerns the structure and role of the set of all possible elastostatic fields in an infinitely long cylinder in the absence of lateral loading and body force, but in the presence of a restriction on the size of a suitable cross-sectional norm of the associated strain tensor field.