On the dynamics of a second-order thin rod

A second-order theory of hyperelastic thin rods is developed from a three-dimensional point of view. The basic topics of geometry and kinematics are given and strain variables are introduced. By means of the virtual work theorem we obtain the equations of motion; the internal work theorem determines the choice of stress variables and, under the hypothesis of hyperelasticity, stress-strain relations are shown. Finally a suitable choice of a second-degree potential, in the Signorini sense, is given.