On constitutive relations for elastic rods

This paper explores the relationships among several existing procedures for specifying linear and nonlinear constitutive relations for hyperelastic Cosserat or directed curves from threedimensional considerations. These procedures are designed to ensure that exact solutions of the balance laws of the directed curve are in approximate agreement with the corresponding exact solutions of classical continuum mechanics. The particular case of the linearized Bernoulli-Euler beam theory is also examined. In addition a new procedure is proposed in this paper. This procedure is used to facilitate comparisons among various existing procedures. Although it is conceptually simple, it illustrates the inherent arbitrariness in specifying constitutive relations for elastic rods.© 1998 Elsevier Science Ltd.