The hinge of bivalve shells can sustain hundreds of thousands of repeating opening-and-closing valve motions throughout their lifetime. We study the hierarchical design of the mineralized tissue in the hinge of bivalve, Cristaria plicata, which endows the tissue with deformability and fatigue resistance, and underlies the repeating motion capability consequently. This folding fan-shaped tissue consists of radially aligned, brittle aragonite nanowires embedded in resilient matrix, and can translate external radial loads to circumferential deformation. The hard-soft complex microstructure can suppress stress concentration within the tissue. Coherent nanotwin boundaries along the longitudinal direction of the nanowires increase their resistance to bending fracture. The unusual biomineral, which exploits the inherent properties of each component through multiscale structural design, provides insights into the evolution of anti-fatigue structural materials.