A composite cord includes a rubber core and a rubber sheath surrounding, at least in part, the rubber core. A formulation of the core is different from that of the sheath. The rubber core includes at least one diene elastomer and more than 30 phr of a filler A. The filler A includes nanoparticles having a weight-average size of less than 500 nm. The rubber sheath includes at least one diene elastomer, from 0 to less than 30 phr of a filler A′, and more than 70 phr of a filler B. The filler A′ includes nanoparticles having a weight-average size of less than 500 nm. The filler B includes microparticles having a weight-median size of greater than 1 μm.