A tire assembly includes a cured tire having a tire cavity and first and second sidewalls extending respectively from first and second tire bead regions to a tire tread region, the first sidewall having at least one bending region operatively bending within a rolling tire footprint and a sidewall groove cut into the cured tire and defined by straight sidewalls and a semicircular bottom positioned within the bending region of the first tire sidewall, the sidewall groove deforming, segment by segment, between a non-deformed state and a deformed, constricted state in response to the deformation of the bending region when adjacent the rolling tire footprint of the tire.