Dipolar gradient elasticity of cables

The increasing structural use of cables and cable-systems has given rise to a substantial technical literature concerning their static and dynamic response. However, the majority of these works is based on classical elasticity theory, according to which the rigidity of the cable is neglected. The present work re-examines in detail the behavior of steel cables under in-plane loading, taking into account the effect of the material microstructure on the overall stiffness, on the basis of the well-established simplified gradient elasticity theory. Accounting for two-dimensional deformations the generalized equilibrium equations under dipolar action are assessed and the corresponding boundary value problem is solved. Numerical results obtained for a characteristic cable segment indicate a much stiffer behavior than the one predicted by classical elasticity theory. This phenomenon is observed in the rod or cable-actuated braking mechanism of bicycles and can be used in novel structural applications.