On the restrictions imposed by non-affine material symmetry groups for elastic rods: application to helical substructures

Abstract

Wire ropes, DNA strands and helical springs are among those bodies which can be modeled as an elastic rod with a helical substructure. The resulting form of the strain-energy function is a matter of material symmetry. This symmetry is explored using a novel treatment which combines non-affine transformations and a relabeling of the material coordinates. The restrictions this treatment imposes on the strain-energy function include a periodic dependency on torsional strain. In addition, comparisons are made with results from a recent treatment of helical symmetry by Healey. Finally, conclusions applicable to material symmetry restrictions for other polar elastic continua are presented.