<p>Materials with J-shaped stress-strain behavior under uniaxial stretching have been developed using various designs; in these materials, the strength increases as the deformation progresses. On the other hand, polymer materials that progressively stiffen under bending are far less explored, and a systematic approach to achieving this behavior has not yet been developed. To address this gap, membrane tensegrity structures, which achieve structural stability by balancing compressive forces in rods and tensile forces in membranes, were examined. Notably, some of these structures exhibit increased stiffness under bending. Using a multipolymer patterning technique, we developed a functional polymer film exhibiting membrane tensegrity-like properties that stiffened under bending. This effect resulted from the membrane tension generated by rod protrusions and a likely increase in the second moment of area at regions with maximum curvature.</p>