A pneumatic tire assembly includes: a tire having a pneumatic cavity; a rigid structure for facilitating operation of the tire assembly, the rigid structure being bonded to the tire by a layered thermoplastic material such that a stiffness gradient is created between the structure and the tire; 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 when radially within a rolling tire footprint; and a sidewall groove defined by groove walls 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 bending of the bending region of the first sidewall while radially within the rolling tire footprint.