A simple remark about the Love hypothesis in rod dynamics

This note discusses the validity of the Love hypothesis in the dynamics of rods, which consists of assuming a linear relationship among the radial and longitudinal strains. In the case of incompressible materials, we show that such an assumption can be correctly employed only within the linear theory of infinitesimal strains. The use of this hypothesis in the nonlinear setting would indeed lead to ‘spurious’ mechanical theories.