The present disclosure relates to a catheter including a torque-transmitting member operatively connected to a functional element of the catheter. The torque-transmitting member may include a flexible structural core, an inner radial layer, and an outer radial layer. The structural core has a plurality of adjacent core segments that move away from one another when the torque-transmitting member is bent along an arc. The inner radial layer has an inner surface secured to the plurality of core segments such that the inner layer experiences localized tensile strain when the core segments at the outer radius of the arc are urged away from one another during bending of the torque-transmitting member. The inner radial layer may comprise an elastomer.