Tire comprising a pair of flexible bead cores

A tire for a motor vehicle, comprising the following in a meridian plane:

• two beads intended to be mounted on a rim;
• two sidewall layers connected to the beads;
• a crown having a tread, the crown having a first side connected to a radially outer end of one of the two sidewall layers and a second side connected to a radially outer end of an other one of the two sidewall layers;
• at least one carcass reinforcement extending from the two beads as far as the crown, the at least one carcass reinforcement having a plurality of carcass reinforcing elements and being anchored in the two beads by way of a turn-up around a bead wire, so as to form a main part and a turn-up in each bead,
• wherein, in each bead, the bead wire has a form of a closed circumferential ring, bracing the bead of the tire against the rim and comprising a first part made up of a first material M1 taking a form of textile cords, the first part interacting with a second part of the bead wire made up of a reinforcing second material M2,
• wherein a tensile stiffness of the bead wire is comprised between 4.5×105 N/m and 1.8×106 N/m,
• wherein a circumferential bending stiffness of the bead wire, Kf, is greater than or equal to Kr*(1000 mm per m*D/(16 in.*25.4 mm per in.))3, where D is a diameter of a wheel on which the tire is mounted, measured at a seat of the rim in meters, and where Kr is equal to 2×10−2 N*m2, and
• wherein an elastic elongation of the bead wire is greater than or equal to 2%.