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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.

A local universal relation is an equation between the stress components and the position vector components which holds for any material in an assigned constitutive family. Although universal relations may be of great help to modellers in characterizing the material behaviour, they are often ignored. In this paper we briefly discuss the valuable insights that universal relations may offer in solid mechanics and determine novel universal relations associated with shearing motions in nonlinearly elastic and nonlinearly viscoelastic materials of differential type.