An Exact Theory of Strain in Rods of Finite Transverse Dimensions

Abstract

<p> An exact analysis for the state of strain in a three dimensional rod continuum is presented. The exact geometrical description of the rod involves the evaluation of a power series expansion of the radius vector. It is shown however, that by a suitable choice of coordinates in the reference configuration and an interpretation of the deformation gradient as a material transformation, the strain tensor may be evaluated to the degree of accuracy inherent in using the full power series expansion of the radius vector without necessitating the explicit evaluation of the power series. Some concepts from the theory of multipolar media are used in order to make this three dimensional analysis compatible with the exact analysis of one dimensional rods.</p>