A novel approach to metamaterial design is introduced through the development of a stable 3D woodpile structure composed of slender cylindrical beams. These beam elements possess diverse bending vibration modes, intricately coupled with propagating waves, leading to complex wave dynamics within the structure. For the efficient analysis of various architectures, an extended discrete element model (DEM) is introduced to accurately emulate the local resonance caused by the beam’s bending vibration modes. The high level of accuracy achieved by the DEM is attributed to the utilization of a physics-informed discrete element modeling approach, rooted in continuum beam theory and wave dynamics within periodic structures. Utilizing the extended DEM, the interplay between propagating waves and local resonance within the beams is investigated, and the adjustability of mode coupling is confirmed by altering the interacting positions of neighboring beams. Subsequent to this, a graded 3D woodpile architecture is designed to progressively superimpose multiple frequency band structures. By adjusting mode coupling, it is shown that the graded woodpile is capable of displaying either a broad frequency passband or a broad frequency bandgap. Further demonstration reveals that the broad frequency bandgap facilitates high-frequency filtering, which effectively attenuates impact waves without the need for additional damping. The stable 3D woodpile architecture proposed in this study shows great potential for practical applications in vibration filtering and impact mitigation across various domains, ranging from small-scale material design to large-scale constructions.