On the theory of porous elastic rods

We consider the direct approach to the theory of rods, in which the thin body is modelled as a deformable curve with a triad of rigidly rotating orthonormal vectors attached to every material point. In this context, we employ the theory of elastic materials with voids to describe the mechanical behavior of porous rods. First, we derive the dynamical nonlinear field equations of the model. Then, in the framework of linear theory, we prove the uniqueness of the solution to the associated boundary-initial-value problem. We identify the relevant field quantities from the theory of directed curves by comparison with the three-dimensional equations of straight porous rods. Finally, for orthotropic and homogeneous rods, we determine the constitutive coefficients in terms of the three-dimensional elasticity constants by solving several problems in the two different approaches.