The transformation between the Lagrangian and Eulerian descriptions of the
equilibrium equations for second-grade elastic materials is reconsidered in the setting
of a convected-coordinate formulation of the relevant kinematics. The third-order
contortion tensor, equivalent to the strain gradient and representing the change of
the Levi-Civita connection induced by deformation, is adopted as the basic
descriptor of the refined kinematics associated with the second-gradient
theory.