Anisotropic frictional model for an object sliding in a granular media

Several locomotion strategies are based on the anisotropic nature of the forces experienced by the moving body with its environment. We report experiments on the anisotropy of the frictional force experienced by a cylinder moving in a granular medium as a function of the orientation $\alpha$ between the cylinder and its velocity. The component of the force in the direction parallel to the velocity of the cylinder is always higher than the perpendicular component and the force is therefore anisotropic. While the parallel component increases continuously with the cylinder angle $\alpha$, we observe that the perpendicular component reaches a maximum value for an orientation of $\alpha_c \simeq 35^\circ$. In order to rationalise these observations, we have developed a theoretical model which assumes that the mechanical energy required to move the cylinder is dissipated by friction and establishes a relationship between the parallel and perpendicular force components that is consistent with experiments.