Tire for vehicle including reinforcements in the sidewalls

A tire comprising:

• a carcass-type reinforcement structure, including reinforcing elements;
• beads, the base of which is configured to be fitted on a rim seat, each bead being extended radially outwardly by a sidewall, the sidewalls meeting radially outwardly with a tread, the intersection of the sidewalls and of the tread defining shoulder ends of the tire;
• under the tread, a crown reinforcement structure;
• in the area of each of the sidewalls, at least one layer of materials having a stretch rigidity in the longitudinal direction greater than 5000 daN/mm, wherein a radially outer end of said layer of materials is radially inside the shoulder ends of the tire;
• and
• on the outer surface of each of the sidewalls, a boss extending circumferentially, the radius of curvature of which is between 8 and 20 mm,
• wherein, for each of the sidewalls, a portion of the carcass-type reinforcement structure has a curvature similar to the curvature of the boss, and
• wherein, for each of the sidewalls, the sidewall radially inside the boss has a first inflection point and the sidewall radially outside the boss has a second inflection point.